It was called the White Australia Policy, and it ended in 1973 (41 years ago). Basically you had to be a white western/northern European who spoke English to immigrate, (essentially British). It's a lot more complicated than that, (of course there's a Wikipedia article about it), but that's the gist of it.

To be clear, there are not inconsiderable number of Australian Aborigines that are 'black'. So presumably you are talking about immigration restrictions and the White Australia policy, which was dismantled in a number of changes between 1966 and 1975 (1996 and the Holt Government's Migration Act, Amendments in 1973 by the Whtilam government, and lastly the 1975 Racial Discrimination Act)