In this paper, electrical characteristics of germanium (Ge) nanowire field effect transistors (FETs) are computationally investigated. A calibrated three-dimensional (3D) density-gradient simulation is performed to explore the electrical characteristics of Ge omega-shaped-gate FETs. The examined nanodevices are with a 70% gate coverage ratio. By evaluating the threshold voltage roll-off, the transfer characteristics, and the leakage current, our numerical results have shown that the Ge nanowire FET has potentially higher driving-capability than that of the silicon (Si) one. Due to good channel controllability of the omega-shaped-gate FET with the 70% gate coverage ratio, compared with the Si nanowire FET, the high mobility Ge nanowire FET significantly suppresses the effect of band-gap narrowing on the transport characteristics. Leakage current of the Ge nanowire FET depends upon the thickness of the gate channel film. A thinner Ge film leads to a lower leakage current. Preliminary numerical study on the Ge Nanowire FET with a propoer selection on gate material provides interesting results for the design and fabrication of high performance nanodevices in nanoelectronics era.