The upper critical field Hc2 appropriate for a pure single crystal with an anisotropic Fermi surface is calculated at low temperatures and is found to have a form Hc2(t)=Hc2(0)×(1+ηt2 ln t), where t=T/Tc. Coefficients Hc2(0) and η are anisotropic reflecting the Fermi surface anisotropy. This expression is a generalization of that for a spherical Fermi surface given by Gor'kov to an anisotropic case.