According to this 1991 Department of Justice study, in 1926 blacks were admitted to prison at 2.94 rate that white people were. By 1986 they were admitted at 5.43 the rate. Time served per conviction has been pretty equal between the races, and hasn't changed much.

But this question is sort of orthogonal to questions of systematic racism in the justice system. We cannot know if either the present or past system is biased against black people solely based on the imprisonment rate. We'd want to know if they are getting equal justice for any given crime. It does seem though, that the higher imprisonment rates historically and in the present are generally reflective of higher crime rates. Here for instance is W.E.B Du Bois in his 1899 book The Philadelphia Negro (p. 259):

It seems plain in the first place that the 4 per cent of the population of Philadelphia having Negro blood furnished from 1885 to 1889, 14 percent of the serious crimes, and from 1890 to 1895, 22 percent. This of course assumes that the convicts in the penitentiary represent with a fair degree of accuracy the crime committed. The assumption is not wholly true ; in convictions by human courts the rich always are favored somewhat at the expense of the poor, the upper classes at the expense of the unfortunate classes, and whites at the expense of Negroes....It has been charged by some Negroes that color prejudice plays some part, but there is no tangible proof of this, save perhaps that there is apt to be a certain presumption of guilt when a Negro is accused, on the part of police, public and judge. All these considerations somewhat modify our judgment of the moral status of the mass of Negroes. And yet, with all allowances, there remains a vast problem of crime.

Similar findings elsewhere in the country are reported by other authors of the early 20th century, such as Ray Stannard Baker's Following the Color Line or Raymond Fosdick's Crime in America and the police.

And when looking at the present day, FBI data the racial breakdown of convictions matches the racial breakdown of offenders from surveying crime victims.

Let’s take a step back here and think about how statistics like these have been used over the past century. The first time these kind of figures became relevant was after the 1890 census, when Frederick Hoffman, an accountant in New Jersey, calculated that blacks accounted for 30% of the nation’s prisoners but only 12% of the population. The conclusion that Hoffman drew – and that many others have drawn, even into the present – is that African Americans have an innate predisposition toward criminality, whether cultural or genetic.

W.E.B. DuBois countered this assertion with a study of black crime in Philadelphia, which he argued was the result of sociological factors – particularly urbanization and industrialization – rather than some innate character trait of black people. Yet the assumption stuck, and even to the present a belief that criminality represents proof and cause of black inferiority remains very strong in American society. (Khalil Gibran Muhammad discusses this at length in his book, The Condemnation of Blackness: Race, Crime, and the Making of Modern Urban America; here’s an interview in which he discusses the 1890 census.)

Yet the higher percentage rate of imprisonment among blacks in 1890 was to a large degree the result of a conscious effort by Southern whites to reduce blacks to a captive, servile labor force through the use of the criminal law. Remember that even though slavery was abolished after the Civil War, most white Southerners did not view its abolition as legitimate and did everything in their power to install a racial order in which blacks would once again be a servile laboring class without political rights – essentially slaves in all but name. This was accomplished in part through the Black Codes, which criminalized African-American behavior that was deemed contrary to this order. For example, many states passed vagrancy laws, which required blacks to sign work contracts for fixed periods – if they were found without these contracts, they would be arrested for vagrancy.

Other states and municipalities passed what some call “pig laws”, turning forms of petty theft from misdemeanors into felonies, allowing for heavy terms of imprisonment for blacks who committed offenses as trivial as stealing a pig – hence the name. (And in many cases, it was not even theft; blacks were engaged in work disputes with landlords and employee, and claimed property they believed was rightfully their own – only to be arrested for the same.)

Law officers were granted a large degree of discretion in enforcing these statutes, and the police were virtually without exception whites with a strong racial bias. What’s more, black prisoners were put to work through the convict lease system, which gave landlords, corporations, states, and municipalities access to very cheap labor, and which played a central role in the industrialization and urbanization of the South at the turn of the last century; about 73% of Alabama's entire annual state revenue came from convict leasing in 1893. So the entire criminal justice system had a vested interest in securing higher rates of arrest, conviction and imprisonment among blacks, both as a source of profit and a means of reinforcing white supremacy.

The heavy involvement of blacks in the criminal justice system, in turn, fostered racial ideas about their inferiority. As Muhammad puts it:

“Defining black criminality through racial and cultural markers of inferiority was at the heart of post-emancipation race relations. Black Codes, Pig Laws, convict leasing, chain gangs, and lynching were direct consequences of inventing new ways of thinking about blacks and using criminal laws, criminal justice practices, and violence to target them—all tracked by statistics, reifying racist presumptions that blacks were an exceptional and dangerous criminal population.” (p. 284)

So starting this discussion in the 1950s is misleading, in that it fails to account for why this association of African Americans and criminality exists - an association that has its origins in Reconstruction and the beginnings of Jim Crow segregation.

(See also the PBS documentary, Slavery By Another Name, based on Douglas Blackmon’s book of the same name.)

(For more on the use of statistics, crime, and race, see this video: https://youtu.be/2xuo32Z2EMA.)