The band line-up and band offset calculations of GaAs0.978Bi0.022/GaAs single quantum well with spatial changes of Bi composition were reported. The spatial Bi profile and a certain amount of the Bi composition in the barrier layer were determined by HR-XRD measurements. Virtual Crystal Approximation and Valence Band Anti-Crossing models were used including strain effects to obtain conduction and valence band edge shifts with Bi incorporation. Photoluminescence (PL) measurements were performed at a low temperature of 8 K as a function of excitation intensity. The PL spectra have shown asymmetric line shapes, which were fitted with different Gaussian functions. Comparing experimental PL results with calculated band edge energies, it was found that optical transition is a type I under low intensity excitation while the optical transition is switched from type I to type II due to the spatial changes in Bi concentrations. The band offsets Delta E-c/Delta E-v were also determined.