  We have investigated the temperature-dependence of the upper critical field
Hc2(T) in a LiFeAs single crystal by direct measurements of resistivity under
static magnetic fields up to 36 T. We find in the case of a magnetic field H
along the ab-plane that Hc2ab(0) = 30 T is clearly lower than the orbital
limiting field Hc2orb,ab (0) = 39.6 T estimated by the |dHc2ab / dT|Tc,
suggesting the presence of both Pauli- and orbital-limiting effects in the pair
breaking process. The best fit of Hc2ab(T) to the Werthamer-Helfand-Hohenberg
formula results in the Maki parameter {\alpha} = 0.9 and negligible spin-orbit
scattering constant ({\lambda}so = 0.0). On the other hand, for H along the
c-axis, Hc2c(T) increases linearly down to our lowest temperature of 0.8 K,
which can be explained by the multi-band effects. The anisotropy ratio Hc2ab(T)
/ Hc2c(T) is 3 near Tc and systematically decreases upon lowering temperature
to become 1.3 at zero temperature. A comparative overview of the behavior of
Hc2ab(T) in various Fe-based superconductors shows that, similar to LiFeAs, the
calculated Hc2orb,ab (0) is generally much larger than the measured Hc2ab(0)
and thus finite {\alpha} values ranging from ~ 0.4 to 3 are necessary to
describe the low temperature Hc2ab(T) behaviors. Moreover, LiFeAs is found to
have the smallest |dHc2ab / dT|Tc values, indicating that LiFeAs is one of the
cleanest Fe-based superconductors with a finite Maki parameter. We also discuss
the implications of multi-band effects and spin-orbit scattering based on the
finding that the estimated Pauli-limiting field is generally much larger than
the BCS prediction in the Fe-based superconductors.
