  We calculate one-loop renormalization factors and mixing coefficients of
bilinear quark operators for a class of gluon actions with six-link loops and
O(a)-improved quark action. The calculation is carried out by evaluating
on-shell Green's functions of quarks and gluons in the standard perturbation
theory. We find a general trend that finite parts of one-loop coefficients are
reduced approximately by a factor two for the renormalization-group improved
gluon actions compared with the case of the standard plaquette gluon action.
