Chief Justice Godfrey Chidyausiku said reasons for rejections would be announced later, The Herald reported.
Prime Minister Morgan Tsvangirai was one of the appellants who asked for the elections to be postponed, the BBC said.
Tsvangirai had argued that the country needed more time to prepare for free and fair elections but said he accepted the court's decision.
President Robert Mugabe and Tsvangirai will face each other again this year in the presidential vote.
The prime minister had pulled out of the second round of the 2008 election after accusing security forces and Mugabe supporters of attacking his own advocates.
Notable deaths of 2014 [PHOTOS]