A spokesman for Bemba said the complaint included seven points challenging the provisional result, which was announced by the electoral commission on Wednesday.
"We are confident that the Supreme Court will give us our result," Delly Sesanga, a laywer and senior member of Bemba's coalition, said after filing the challenge. Bemba's camp has already denounced "systematic cheating" in the count.
"We think that there have been many irregularities in the process and it hasn't been democratic and transparent."
Bemba has complained about a special dispensation for people such as electoral workers and party representatives allowing them to vote in the polling station where they were working rather than where they were registered.
The challenge also said results had been falsified, party representatives were blocked from polling stations where they were meant to observe the vote, and ballot boxes were stuffed.
The complaint also questioned high voter turnout figures in eastern Congo, which is Kabila's home and which overwhelmingly supported him in both rounds of voting.
Bemba has broad support in Kinshasa and the rest of western Congo, which speaks his Lingala tongue as opposed to the Swahili spoken by Kabila and most other easterners.