Quasiclassical trajectory and quantal calculations are carried out for the Penning ionization system N-2+He*(2(3)S)-->N-2(+) ((2) Sigma(g), (2) Pi(u), (2) Sigma(u))+He+e(-) based on an ab initio resonance potential and 2 energy widths which were obtained in previous work. Total and partial ionization cross sections are evaluated for the collision energy range of 0.1-1.0 eV. For the trajectory calculation, the collisional energy dependence of the cross section is in better agreement with a recent experiment on state resolved Penning ionization than calculations using the classical sudden approximation. The result in the high frequency rotation limit is significantly different from that for the sudden approximation, which is in contrast to the H-2-He* system. The results for quantal calculations using the sudden and spherical-potential approximations confirm the reliability of classical treatments. The results obtained suggest that analyses with the widely used atomic-target models lose their validity for significantly anisotropic systems in which targets have large moments of inertia.