Solicitors Mike Dailly and Austin Lafferty aim to raise £150,000 to fund the scheme for three years in Cameroon.
The two lawyers believe access to justice will play a huge role in developing the community they have targeted, Bamenda, the capital of the nation's north-west region and a major centre for child trafficking.
The centre will be run by Laura Anyola Tufon, Cameroon's human rights commissioner.
She said: "This project will be a life time reward to our poverty-stricken, legally uneducated and destitute populations in demand for justice.
"It will help curb corruption to a remarkable level as the target populations will be knowledgeable to work to uphold human rights and abusers will be brought to justice. My dream of rights conscious citizens and peace abiding people with ambition to contribute to sustainable development and make life worth living may be met in my life time."
Mr Dailly, who runs the Govan Law Centre in Glasgow, said: "I've already undertaken an extensive scoping project in Cameroon and helped secure initial funding for a Child Protection Unit from the British High Commission in Yaounde, operated by local justice activists in Bamenda.
"That project helped reunite victims of human trafficking with their families. Child and adult trafficking in Cameroon is most prevalent in the north-west region of the country.
"The law centre would help tackle human trafficking, secure criminal prosecutions, recover unpaid wages and protect the rights of women and children."
Austin Lafferty, a former president of the Law Society, said: "There is an overwhelming need and widespread national support for a community law centre in Bamenda.
"Scottish solicitors have trailblazed legal remedies and campaigns which have benefited Scots, and I'd like to see those successes replicated in Africa.
"The project would provide a pilot to demonstrate the value of the model with a view to securing repetition in the country."