His wife Kaniz Fatema Mostaq is the president of Cox's Bazar District Women's Awami League and the chairman of Cox's Bazar Jatiya Mohila Songstha.
[3] Mostaq Ahmad Chowdhury is the chairman of Cox's Bazar district council.
He was earlier the administrator of Cox's Bazar district council.
In the 1970, he was elected as an MP for the first time as an independent candidate from the then Chittagong-17 (Cox's Bazar Sadar-Ramu) constituency.
He was re-elected as an MP from Cox's Bazar-3 (Sadar-Ramu) constituency in the fifth national election in 1991.