A hydrogen supply apparatus of fuel cell stack is provided. In particular, a plurality of unit cells includes a membrane electrode assembly, a separating plate disposed on two sides of the membrane electrode assembly, a coolant path, an air path, a fuel path, and an air inlet manifold communicated with the air path. An end plate is disposed on each end of the plurality of unit cells and forms an air inlet manifold in a location corresponding to the air inlet manifold of the separating plate. Additionally, a hydrogen supply apparatus is provided in the air inlet manifold of the separating plate and the air inlet manifold of the end plate that selectively supplies additional hydrogen to the cathode through the air path when needed.