Using density functional theory with Hamprecht–Cohen–Tozer–Handy (HCTH) functional, we demonstrate that the electric bias V applied on the surfaces of 〈112〉 Si nanowires (SiNWs) can modulate longitudinal (bandgap Eg) and transverse (indirect to direct bandgap transition) variations of electronic band structures while the latter is direction-dependent and occurs only when V is applied on (110) layers. The physical mechanism of the variations of electronic band structures is essentially the electron redistribution in different layers. Also the semiconductor-to-metal transition can be realized where SiNWs go into metallic regime under suitable values of electric bias. The density of states near the Fermi level increases with increasing V after a semiconductor to metal transition occurs in SiNWs. These results extend the application of SiNWs in optical and electronic nanodevices.