We have performed a comparison study of the Rydberg-state excitation of model molecules (1πg and 1πu states) in different laser fields by the approaches of time-dependent Schrödinger equation and a fully quantum-mechanical model, and both simulations show good accordance. It is found that the peak structure of the Rydberg-state population vs laser intensity becomes pronounced for longer laser pulses due to the stronger interference effect between the subwave packets released in different optical cycles, and the locations of the intensity-dependent peaks closely satisfy the multi-photon resonant transition condition. In addition, it is demonstrated that the populations of the Rydberg states possessing the identical parity oscillate in an inverse manner with increasing laser intensity for different initial states (1πg and 1πu), and the aforementioned distinct phenomenon is attributed to the additional phase introduced by the symmetry of 1πg state with respect to that of 1πu state.