GaAsSb/GaAs single quantum wells (SQWs) grown by molecular beam epitaxy are studied by selectively-excited photoluminescence (SEPL) measurement. For the first time, we have simultaneously observed the PL from both type Ⅰ and type Ⅱ transitions in GaAsSb/GaAs heterostructure in the SEPL. The two transitions exhibit different PL behaviours under different excitation energy. As expected, the peak energy of type I emission remains constant in the whole excitation energy range we used, while type Ⅱ transition shows a significant blue shift with increasing excitation energy.The observed blue shift is well explained in terms of electron-hole charge separation model at the interface. Time-resolved(TR) PL exhibits more type Ⅱ characteristic of GaAsSb/GaAs QW. Moreover, the results of the excitation-power-dependent PL and TRPL provide more direct information on the type-Ⅱ nature of the band alignment in GaAsSb/GaAs quantum-well structures. By combining the experimental results with some simple calculations, we have obtained the strained and unstrained valence band offsets of Qv＝1.145 and Q0v＝0.76 in our samples, respectively.