Alpha Mchunu played football in an amateur capacity. In the early 1980s he became chairman of a club in the Inter Association in Durban.
Mchunu served on the disciplinary committee of the Durban and Country Football Association. He was elected to serve in the Provincial structure as the assistant secretary under the leadership of Qokololo Hlophe in KZN Unity Football. Mchunu was a member of the South African Football Association and National Football Association. After the merging of the two associations in 1996, he became Secretary of Southern KwaZulu Natal Football Association.
In 1999 he was elected as the President of SAFA (Southern KwaZulu Natal Football Association). He was then appointed the Chairperson of KwaZulu Natal Academy of Sport, where he still serves as the chairperson. In 2000 he became the Commercial General Manager of AmaZulu Football Club. After the demarcation of the structure of SAFA from four regions of KwaZulu Natal into 52 regions, SAFA Southern KZN became the eThekwini Region under Municipality boundaries; he was elected the President of SAFA eThekwini Region in 2006 and to date. In the same year he was elected to the SAFA National structure in Johannesburg. In 2009 he became the Deputy Head of SAFA National as the convener of referees. Alpha Mchunu has been at the helm of SAFA eThekwini for a long time.