MRG says there have been major human rights crises in the last decade
The African Court on Human and Peoples' Rights, set up 10 years ago, has yet to hear a single case, according to campaigners at Minority Rights Group.
The report by the group says this is despite human rights crises including Darfur, the Democratic Republic of Congo and Zimbabwe.
It blames a lack of political will on the continent.
Only 24 of 53 African Union member countries have ratified the protocol creating the court in 1998.
According to the MRG report being launched in the Ugandan capital, Kampala, an effective pan-African court is crucial because minorities and indigenous peoples often fail to receive justice from national legal systems.
"Africa's peoples deserve better. If human rights on the continent are to come of age, the court must start its work without any further delays," the report's author George Mukundi said in a statement.
No case has yet been heard although judges have been appointed, the rules of procedure agreed and a location established in Arusha, Tanzania.
The group also blames bureaucracy for the slow start.