In this paper, we design a biaxial tensile strained GeSn photodetector with fin structure wrapped in Si(3)N(4) liner stressor. A large biaxial tensile strain is induced in GeSn fins by the expansion of Si(3)N(4) liner stressor. The distribution of tensile strain in GeSn fins was calculated by a finite element simulation. It is observed that magnitude of the strain increases with the reduction of fin thickness T(fin). Under the biaxial tensile strain, the direct band gap E(G,Γ) of GeSn fin photodetector is significantly reduced by lowering Γ conduction valley in energy and lifting of degeneracy of valence bands. As the 30 nm Si(3)N(4) liner stressor expanses by 1%, a E(G,Γ) reduction of ~0.14 eV is achieved in Ge(0.92)Sn(0.08) fins with a T(fin) of 100 nm. The cut-off wavelengths of strained Ge(0.96)Sn(0.04), Ge(0.92)Sn(0.08) and Ge(0.90)Sn(0.10) fin photodetectors with a T(fin) of 100 nm are extended to 2.4, 3.3, and 4 μm, respectively. GeSn fin photodetector integrated with Si(3)N(4) liner stressor provides an effective technique for extending the absorption edge of GeSn with Sn composition less than 10% to mid-infrared wavelength.