Russian police detained opposition activists on Friday and warned they would break up any illegal rallies this weekend.
However, no detentions were seen at the protest on Saturday.
About 400 hundred people, including journalists, joined the protest, the Interfax news agency quoted Moscow police as saying.
A Reuters witness estimated the number of people at the protest at around 1,500.
The final election results were released on Friday and handed the ruling United Russia party that backs President Vladimir Putin 324 of the State Duma's 450 seats.
The Kremlin has said it wants electronic voting, which was used in Moscow for last week's election as well as several other regions, to be rolled out nationwide in future votes.
The election was held in accordance with the law, the RIA news agency quoted Putin as saying at a meeting with leaders of the Duma parties on Saturday.