  We investigate the superconducting mechanism and the transition temperature
of heav y fermion superconductor UPd_2Al_3 on the basis of a single band
two-dimensional Hubbard model on triangular lattice, whi ch represents the most
heavy band of UPd_2Al_3. Both normal and anomalous self-energies are calculated
up to third order with respect to the Coulomb repulsion U between itinerant
electrons. The superconducting transition temperature is obtained by solving
the Eliashberg's equation. Reasonable transition temperatures are obtained for
moderately large U. It is fou nd that the momentum and frequency dependence of
spin fluctuations given by RPA-like terms gives rise to the d-wave pairing
state, while the vertex correction terms are important for obtaining reasonable
transition tempe ratures. These results seem to show that the superconductivity
in UPd_2Al_3 can be explained by the perturbation theory with respect to U.
