Abstract: Based on the k·p perturbation theory, the 8-band Kane model and 8-band Lüttinger-Kohn model are effective means for calculating the mini-band structures of type Ⅱ superlattices, and are commonly used in the design of type Ⅱ superlattice materials and device structures. Base On the eight-band k·p model, the total Hamiltonian matrix for long-wavelength InAs/GaSb superlattices and medium-wavelength InAs/GaSb superlattices are constructed separately using the finite difference method based on non-uniform discretization. The numerical solution of the dispersion relation for the superlattice within the wavevector space are obtained by calculating the eigenvalues of the Hamiltonian matrix. This process shows the structure of mini-bands adjacent to the Γ point for both the long- and medium-wavelength InAs/GaSb superlattice. The effective band gaps of the medium-wavelength and long-wavelength superlattices are determined to be 0.247 eV and 0.109 eV, respectively. These values are consistent with both the uniform discretization calculations and the 100% cutoff wavelength measurements. Compared with the uniform discretization, the non-uniform discretization can save a significant amount of computation time in the InAs/GaSb superlattice mini-band calculation while ensuring accuracy.