Compton profiles of momentum distribution of conduction electrons in the orthorhombic phase of α-Ga metal at low temperature are calculated in the band model for the three crystallographic directions (100), (010), and (001). Unlike the results at room temperature, previously reported by Lengeler, Lasser and Mair, the present results show strong anisotropy in the Compton profiles with the momentum distribution along (001) direction being substantially different from the other two directions. While experimental data on Compton profiles at low temperatures are not available for comparison with theory, the resistivity data in α-Ga at low temperature strongly support this anisotropic behaviour. Besides, the electronic heat capacity constant γ available from both experiment and present calculation suggests that the conduction electron distribution at low temperature in the orthorhombic phase is markedly different from the free-electron-like-distribution at room temperature, thus lending additional support to anisotropic behaviour of Compton profiles. It would be nice to have Compton profiles data from experiment at low temperature for direct comparison with theory. It is hoped that the present work would stimulate enough interest in that direction.