Type-II InAs/GaSb superlattices made of 13 InAs monolayers (MLs) and 7 GaSb MLs are grown on GaSb substrates by solid source molecular beam epitaxy. To obtain lattice-matched structures, thin InSb layers are inserted between InAs and GaSb layers. We complete a series of experiments to investigate the influence of the InSb deposition time, V/III beam-equivalent pressure ratio and interruption time between each layer, and then characterize the superlattice (SL) structures with high-resolution x-ray diffraction and atomic force microscopy. The optimized growth parameters are applied to grow the 100-period SL structure, resulting in the full-width half-maximum of 29.55 arcsec for the first SL satellite peak and zero lattice-mismatch between the zero-order SL peak and the GaSb substrate peak.