The plasticity of GeSn alloy energy band has promoted the development of silicon-based photoelectric integration and optical interconnection. A tensile-strained GeSn/SiGeSn double heterostructure laser wrapped with Si3N4 stress liner is designed and characterized theoretically. The triaxial tensile strain is introduced into the GeSn/SiGeSn heterostructure laser by the Si3N4 linear stressor. The lower threshold current density and higher optical gain of the GeSn/SiGeSn laser can be achieved by tuning the band structure and carrier distribution in the active region with tensile strain and Sn compositions. Compared with the relaxed device, the value of ne
,Γ/ne
,total for the Ge0.90Sn0.10/Si0.315Ge0.499Sn0.186 heterostructure laser wrapped with 300 nm Si3N4 linear stressor is increased to 30.6% at n
e,total of 1018 cm−3, the laser λ can be extended to 3.44 μm, and the J
th is reduced from 206 to 59 A/cm2.