The band structures of wurtzite-AlN/InN and AlN/GaN superlattices are calculated by the Krnig-Penney model and the deformation potential theory under considering the lattice strain. Our calculations include the variation of band structure with the parameters for the sublayers, and the energy dispersion relations. It is found that by varying the sublayer thickness, the band structures can be well designed in different ways. The strain will change the bandgaps, reduce the band offsets and the sub-bands obviously, and make the valence band more complex. In comparison with the experimental results, our model is rather suited for simulating the narrow-quantum-well structures, while for the wide-quantum-well structures, the build-in field should be considered.