In photoluminescence (PL) spectra of a ZnS-ZnTe superlattice grown on GaAs substrate a multi-band structure with equal energy spacing of about 90meV has been observed. This multi-band structure is shown to be explainable with a one-dimensional harmonic oscillator model where electrons and holes are confined separately in approximately parabolic potential wells formed by space charges at the p-n heterojunctions. The origin of the PL spectrum is attributed to electron-hole recombinations from electrons being in Boltzmann distribution among levels n = 0, 1, 2,... in n-ZnS to the holes at n = 0 level in p-ZnTe. However. an appreciably higher electron temperature than the lattice temperature is necessary for explaining the observed spectral shape, although the temperature during decay shows a tendency of cooling down. Thermal quenching of the luminescence as a whole is thought to be due to hole release from the level in ZnTe.