Recently, germanium nanowires (Ge NWs) have been studied extensively and a variety of applications have been reported. Moreover, lately Ge NWs are also considered as a promising material for Si-compatible photonic devices. However, similar to its bulk counterpart, most of Ge NWs have indirect band gap, which is not favorable for optical transitions. Due to quantum confinement effects, Ge NW exhibits unique properties that different with their bulk counterparts, e.g. tunable band gaps by varying the diameter. While studies about indirect-to-direct band gap engineering in bulk Ge have been extensively conducted, the studies about indirect-to-direct band gap engineering in Ge-based nanowires are still limited. In this work, we investigate the electronic structures of -oriented Ge/Sn core-shell NWs through first-principles density functional calculations. The lattice mismatch between Ge and Sn induces intrinsic tensile strain on Ge core and drives an indirect-to-direct band gap transitions. The band gaps of Ge/Sn core-shell NWs can be tuned by controlling the core-to-shell ratio and the diameter of NWs. Furthermore, we show that an external tensile strain along the  direction can trigger indirect-to-direct band gap transitions for NWs with the intrinsically indirect band gaps. The critical strains are significantly reduced, as compare to pure Ge NWs with the diameter similar to the core sizes. The matrix element of direct optical transitions is examined and we confirm that all the direct band gaps are dipole-allowed.