Alexander Kobina Baah Ampiah is a retired Ghanaian Supreme Court Judge. He served on the Supreme Court bench from 1993 to 2003. Prior to serving on the Supreme Court bench, he was a lawyer who rose through the ranks as a judge of the High Court to the bench of the Appeals Court of Ghana.

Ampiah studied law in the UK. He qualified as a barrister and practiced privately at Aumog chambers. He rose through the ranks from a High Court judge to an Appeals Court judge prior to his appointment to the Supreme Court Bench on 6 January 1993.

While in the judiciary service, he served as the president of the Ghana Football Association (GFA) Congress, the highest decision-making body of the association. Ampiah retired as a Supreme Court Judge on 25 July 2003.

In 2009 he was appointed chairman of the University of Cape Coast council by the then president of Ghana; John Evans Atta Mills. In 2011 he was awarded the Order of the Volta award for his service to the nation.