Using effective-mass Hamiltonian model of semiconductors quantum well structures, we investigate the electronic structures of the -conduction and L-conduction subbands of GeSn/GeSiSn strained quantum well structure with an arbitrary composition. Our theoretical model suggests that the band structure could be widely modified to be type I, negative-gap or indirect-gap type II quantum well by changing the mole fraction of -Sn and Si in the well and barrier layers, respectively. The optical gain spectrum in the type I quantum well system is calculated, taking into account the electrons leakage from the -valley to L-valley of the conduction band. We found that by increasing the mole fraction of -Sn in the barrier layer and not in the well layer, an increase in the tensile strain effect can significantly enhance the transition probability, and a decrease in Si composition in the barrier layer, which lowers the band edge of -conduction subbands, also comes to a larger optical gain.