In this paper, the composition profiles within intermixed AlInGaAs-based multiple quantum wells structure are analyzed by secondary ion mass spectrometry and the bandgap blue shift is found to be mainly attributed to the interdiffusion of In and Ga between the quantum wells and barriers. Based on these results, AlInGaAs-based single quantum well structures with various compressive strain (CS) levels are then investigated and we report an enhancement of the bandgap shift by increasing the compressive strain level in the SQW. For instance, at an annealing temperature of 850 degrees C, the photoluminescence blue shift can reach more than 110 nm for the sample with 1.2%-CS SQW, but only 35 nm with 0.4%-CS SQW. The indium composition ratios are designed to be 0.59 and 0.71 for the 0.4% and 1.2%-CS quantum wells, respectively, as opposed to 0.53 for the lattice-matched barrier. This relatively larger atomic compositional gradient between the CS quantum well and barrier is expected to facilitate the atomic interdiffusion and lead to the more pronounced bandgap shift.