Electronic structures and band structures of a series of InAs/GaSb superlattice in (111) orientation were calculated by density functional theory (DFT) method. Heyd-Scuseria-Ernzerhof (HSE) hybridization coupled with revised Perdew-Burke-Ernzerhof (PBE) approximation for solids and surfaces (PBEsol) showed better consistency with the experimental measurements than conventional DFT and several compared hybrid functionals. The bandgap changes with periodic thickness and InAs/GaSb ratio of InAs/GaSb superlattice. The results are in good agreement with the former experimental researches. These results indicate the feasibility of HSE coupled with PBEsol method in prediction of the electronic properties of InAs/GaSb superlattice.