Semiconductor nanowires, based on silicon (Si) or germanium (Ge) are leading candidates for many ICT applications, including next generation transistors, optoelectronics, gas and biosensing and photovoltaics. Key to these applications is the possibility to tune the band gap by changing the diameter of the nanowire. Ge nanowires of different diameter have been studied with H termination, but, using ideas from chemistry, changing the surface terminating group can be used to modulate the band gap. In this paper we apply the generalised gradient approximation of density functional theory (GGA-DFT) and hybrid DFT to study the effect of diameter and surface termination using –H, –NH2 and –OH groups on the band gap of (001), (110) and (111) oriented germanium nanowires. We show that the surface terminating group allows both the magnitude and the nature of the band gap to be changed. We further show that the absorption edge shifts to longer wavelength with the –NH2 and –OH terminations compared to the –H termination and we trace the origin of this effect to valence band modifications upon modifying the nanowire with –NH2 or –OH. These results show that it is possible to tune the band gap of small diameter Ge nanowires over a range of ca. 1.1 eV by simple surface chemistry.