  Detailed Fermi-surface structures are essential to describe the upper
critical field $H_{c2}$ in type-II superconductors, as first noticed by
Hohenberg and Werthamer [Phys. Rev. {\bf 153}, 493 (1967)] and shown explicitly
by Butler for high-purity cubic Niobium [Phys. Rev. Lett. {\bf 44}, 1516
(1980)]. We derive an $H_{c2}$ equation for classic type-II superconductors
which is applicable to systems with anisotropic Fermi surfaces and/or energy
gaps under arbitrary field directions. It can be solved efficiently by using
Fermi surfaces from {\em ab initio} electronic-structure calculations. Thus, it
is expected to enhance our quantitative understanding on $H_{c2}$. Based on the
formalism, we calculate $H_{c2}$ curves for Fermi surfaces of a
three-dimensional tight-binding model with cubic symmetry, an isotropic gap,
and no impurity scatterings. It is found that, as the Fermi surface approaches
to the Brillouin zone boundary, the reduced critical field $h^{*}(T/T_{c})$,
which is normalized by the initial slope at $T_{c}$, is enhanced significantly
over the curve for the spherical Fermi surface with a marked upward curvature.
Thus, the Fermi-surface anisotropy can be a main source of the upward curvature
in $H_{c2}$ near $T_c$.
