Obaidul Ghani’s grandfather, Maulvi Elahad, had moved from Darbhanga, Bihar to Calcutta in the mid-19th century. After obtaining his M.B.B.S. degree he founded the Park Circus charitable dispensary in 1950, serving the poor and lower middle-class populations of the city. Obaidul Ghani contested the 1952 West Bengal Legislative Assembly election as an independent, standing in the Baniapukur Ballygung constituency. He obtained 524 votes (0.88%).
Obaidul Ghani represented the Entally constituency in the West Bengal Legislative Assembly 1957–1971, standing as a CPI candidate in the 1957, 1962, 1967 and 1969 elections. As a politician, he obtained significant popularity for his provision of medical services to the poor people of Calcutta. He stayed with CPI in the 1964 split. In August 1969 the Modern Furnishers Mazdoor Union was registered, with Obaidul Ghani as its president. The union was affiliated to the All India Trade Union Congress.
He lost the Entally seat to Mohammed Nizamuddin of the Communist Party of India (Marxist) in the 1971 West Bengal Legislative Assembly election. He managed to defeat Mohammed Nizamuddin in the 1972 West Bengal Legislative Assembly election and regained the Entally seat.