In this work, the molecular structure and energy of some critical points in nonradiative relaxation process of the excited state of pentafluoropyridine are studied through quantum chemistry calculation. The structures and the vertical excitation energies and adiabatic excitation energies of the ground state and two lowest exited states are calculated. The geometry of the ground state is a planar structure with C_2v symmetry, while the geometries of the two lowest excited states are half-boat structures with out-of-plane distortions. Furthermore, the topology structures and energy of the conical intersections of S₂/S₁, S₁/S₀ and S₂/S₀ are determined. The topology structures of the conical intersections S₂/S₁, S₁/S₀ and S₂/S₀ in the branching space are all peaked with asymmetric structures, and are determined to be structure of boat, half-boat, and chair, respectively. Their corresponding energy values are estimated at 6.39, 5.16 and 8.51 eV, respectively. The results show that the primary non-adiabatic relaxation pathway is the wavepacket of the S₂ state rapidly evolving into the S₁ state via the S₂/S₁, and then directly relaxing to the ground state via the S₁/S₀. In addition, the probability of directly relaxing to the ground state through S₂/S₀ is smaller.