By numerically solving the time-dependent Schr\"odinger equation, we theoretically investigated the dynamic interference in multiphoton excitation and ionization of hydrogen irradiated by 400-nm linearly polarized laser pulses. Interference of the multiphoton excitation paths at the rising and falling edges of the laser pulses gives rise to the fast oscillations of the intensity-dependent yield of the excited states. Our results show that the period of the oscillation increases abruptly when the laser intensity increases above the eight-photon ionization threshold. By tracing the population evolution of the ground state, we find that the depletion of the ground state on the rising edge of the laser pulse closes the multiphoton excitation path at the falling edge of the pulse. The slower oscillation comes from the interference of the excitation paths at different instants during the rising edge of the laser pulses. The change in the interference paths in the high-laser-intensity region also occurs in multiphoton ionization. The photoelectrons released at different instants of the rising edge of the laser pulses possess different parities. This difference is imprinted in the up-down asymmetry along the laser polarization direction in the photoelectron momentum distribution. The dynamic interference of the Rydberg states provides rich information about the dynamics in strong-field ionization.