  We study the pairing symmetry of a doped Kane-Mele model on a honeycomb
lattice with on-site Coulomb interaction. The pairing instability of Cooper
pair is calculated based on the linearized Eliashberg equation within the
random phase approximation (RPA). When the magnitude of the spin-orbit coupling
is weak, even-frequency spin-singlet even-parity (ESE) pairing is dominant. On
the other hand, with the increase of the spin-orbit coupling, we show that the
even-frequency spin-triplet odd-parity (ETO) f-wave pairing exceeds ESE one.
ETO f-wave pairing is supported by the longitudinal spin fluctuation. Since the
transverse spin fluctuation is strongly suppressed by spin-orbit coupling, ETO
f-wave pairing becomes dominant for large magnitude of spin-orbit coupling.
