The main objective of this paper is to comprehensively study influences of the variation of the bottom profile inside the harbor on the transient harbor oscillations excited by normally-incident N-waves. The specific physical phenomena investigated consist of wave profile evolution, maximum runup, relative wave energy distribution and total wave energy inside the harbor. A series of numerical experiments are implemented using a fully nonlinear Boussinesq model, FUNWAVE-TVD. Results show that when the harbor is subjected to the leading-elevation N-waves (LEN waves), the evolution of the maximum free surface elevation during the wave shoaling process inside the harbor coincides well with Green's law overall. When the incident wave amplitude is small, the maximum runup inside the harbor is almost only determined by the incident wave amplitude. As the incident wave amplitude increases, effects of the bottom profile on the maximum runup closely depend on both the incident wave type and amplitude. As the mean water depth inside the harbor decreases, the relative wave energy distribution tends to become more uniform, regardless of the incident wave amplitude and type. Finally, the variation trend of the total wave energy with the bottom profile is found to depend on the incident wave amplitude.