In this work, relaxed GeSn p-channel tunneling field-effect transistors (pTFETs) with various Sn compositions are fabricated on Si. Enhancement of on-state current ION with the increase of Sn composition is observed in transistors, due to the reduction of direct bandgap EG. Ge0.93Sn0.07 and Ge0.95Sn0.05 pTFETs achieve 110% and 75% enhancement in ION, respectively, compared to Ge0.97Sn0.03 devices, at VGS - VTH = VDS = - 1.0 V. For the first time, ION enhancement in GeSn pTFET utilizing uniaxial tensile strain is reported. By applying 0.14% uniaxial tensile strain along [110] channel direction, Ge0.95Sn0.05 pTFETs achieve 12% ION improvement, over unstrained control devices at VGS - VTH = VDS = - 1.0 V. Theoretical study demonstrates that uniaxial tensile strain leads to the reduction of direct EG and affects the reduced tunneling mass, which bring the GBTBT rising, benefiting the tunneling current enhancement in GeSn TFETs.