We address the perturbative renormalization of massive lattice fermion
s. We derive expressions-valid to all orders in perturbation theory an
d for all values of the bare fermion mass-for the rest mass, the kinet
ic mass, and the wave-function renormalization factor. We obtain the f
ermion's self energy at the one-loop level with a mass-dependent, O(a)
improved action. Numerical results for two interesting special cases,
the Wilson and Sheikholeslami-Wohlert actions, are given. The mass de
pendence of these results smoothly connects the massless and infinite-
mass limits, as expected. Combined with Monte Carlo calculations our r
esults can be employed to determine the quark masses in common renorma
lization schemes. [S0556-2821(98)04515-9].