The optical gain and the luminescence of a ZnO quantum well with MgZnO barriers is studied theoretically. We calculated the non-Markovian optical gain and the luminescence for the strained-layer wurtzite quantum well taking into account of the excitonic effects. It is predicted that both optical gain and luminescence are enhanced for the ZnO quantum well when compared with those of InGaN-AlGaN quantum well structure due to the significant reduction of the piezoelectric effects in the ZnO-MgZnO systems.