To investigate the gain characteristics of optically pumped vertical external cavity surface emitting lasers, taking InGaAs/GaAs strained quantum wells as an example, a complete system model which considers all the effects of the band-gap, band-edge discontinuities and band structure is established. In view of the valence band mixing and the wave function mixing, the 6×6 effective-mass Luttinger-Kohn Hamiltonian is solved by using the finite difference method, and the conduction-band structures, the valence-band structures and envelope functions are obtained. And then the material gain and spontaneous radiation spectrum with linear Lorentzian function are simulated numerically. Finally, the effects of the well width, carrier density, temperature and other factors on the quantum-well gain are discussed. The calculated results provide a theoretical basis for the optimized design of optically pumped vertical external cavity surface emitting lasers.