InGaAs strained quantum wells (QWs) with GaAs, AlGaAs, and GaAsP barriers are widely used in optically pumped vertical-external-cavity surface-emitting lasers operating at 1 μm wavelength band. Compared with the reported data, the model-solid theory, which is more suitable for the studied materials, is selected to calculate the band offset. The band structures and the gain characteristics of the three different QWs are computed and compared, and the theoretical results are in good agreement with the recent experimental reports. The numerical simulation shows that the QW with the GaAs barrier has the highest absorption but the lowest peak gain, while for the AlGaAs barrier, it has the lowest absorption but the highest peak gain, and for the GaAsP barrier, it has a moderate absorption and peak gain. GaAsP is the most appropriate candidate for the barrier of InGaAs strained QW when the low-threshold, large-gain, and high-temperature characteristics are demanded simultaneously.