China is still governed by the Communist party (though you could say that they have largely abandoned Communist economic principles for the last several decades) and they are being quite "successful" across many definitions of "success".
Stalin's USSR was "successful" in defeating Nazi Germany in WWII.
In general you will need to define "successful" and "communist" more precisely to get meaningful answers to this question.
If we define "success" in terms of economic performance, and "communist" in terms of a (near totally) centrally planned economy, then there seems to be evidence that such a system can be very successful over a relatively short period. (one to several decades).
As witness the USSRs economic growth over several of their 5 year plans.
A centrally planned economy seems to work fairly well in delivering efficiency and growth within a know and static set of technologies.
Over longer periods, the centrally planned economy seems to be extremely poor at innovation and reallocation of resources from older industries and technologies to newer ones.
Given longer timescales than one or two decades, central planning of economic activity seems to dramatically under perform vs. the competitive model of capitalism.
Since your question is not clearly defined, im just gone assume some things:
With communist you mean "central planning economy" since that is what most people mean when they say "communist"
With "successful" you mean that ordanary people have a increasing standard of living over time (and I would assume that you would think civil freedoms like free speech and such are importent)
Now assuming these things the answer comes out to be, not really.
There are are people pointing to the success of stalin to industrialise the soviet union or simular episodes of growth. But generally growth in output does not actually mean that anybody has a better live. To achive these successes mass mobilistaion of the population (including large amount of farmers) for hard work and little pay. Private consumtion like housing and consumer products was very low. Also many millions of people died and many were literally forced to work or face death.
In later priodes that USSR moved its focus away from pure heavy industrialistion and focused more on consumers. However this did not produce a wastly grwoing economy, more a stable economy that did not evolve all that much. Consumer consumption stayed much lower as well.
There can be simular stories for most other top down economies.
The best that can be said for some communist countries is that they dont decline and crash but are rather stable and to achive some limited success.
Most people that used to push ideals like "market socialism" and "top down central planning" have switched over to advocating the advocating the model of the scandinavian countries. A large governemnt and social safety balanced by a market. Denmark for example has a very large governemnt but also a very free market in the rest of the economy. While this is not communism/socialism as socialist/communist thinkers thought about them, they do solve many of the same problems they were worried about.