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We propose and analyze a strain-balanced GezSn1-z-SixGeySn1-x-y multiple-quantum-well (MQW) laser. By incorporating a proper amount of -Sn into Ge, a direct-bandgap GeSn alloy can be realized to achieve population inversion in the direct conduction band. The introduction of compressive strain into the GeSn QW can effectively modify the valence band structure to reduce the threshold carrier density. We calculate the electronic band structure and the polarization-dependent optical gain of the strained GezSn1-z-SixGeySn1-x-y MQW laser taking into account the effect of the L-conduction bands. We also present our waveguide design for index guidance and calculate the optical confinement factors of various regions. Our calculation indicates that the modal gain can reach the threshold condition and lead to lasing action.