The wave-packet dynamical approach was used to investigate the excited-state intramolecular proton transfer (PT) of 5’-amino-2-(2’-hydroxyphenyl) benzimidazole (P1) based on the relaxed potential surfaces. For the involved PT process of P1 molecule, the quantum chemical calculation shows that relative to the ground state S0 with a single potential well, the excited state S1 with a double potential well can give much dynamical information. It is also found that because of the existence of a shallow potential barrier on the excited state S1, the PT in it is much easier than that in the ground state S0. When a laser field is used to pump the wave packet and induce the PT process, the external field parameters, such as the frequency and the envelope, have also influences on the PT process because of the impact of both pump time and the energy gap between two states. This kind of external field effect on the PT process gives a specific perspective to examine its dynamical mechanism and provides a reference for exploring the light-induced biophysical processes.