We investigate the quantum-phase dynamics of a dissipative molecular system interacting with a single-mode amplitude-squeezed field (with a sub-Poissonian photon-number distribution) using the Monte Carlo wave-function method. As quantum dissipation, we consider molecular coherent (phase) and population relaxations, which are caused by nuclear vibration, and cavity relaxation (the dissipation of an internal single mode to outer mode). In this study, we elucidate the effects of these dissipations on the unique quantum dynamical behaviors of this coupled system, e.g., collapse-revival behavior of Rabi oscillations, using the quasiprobability (Q function) distribution of a single-mode field and the off-diagonal molecular density matrix. It is found that although the amplitude-squeezed field exhibits a distinct revival with larger amplitudes of molecular population in the presence of the molecular phase and population relaxations as compared to the coherent field, a very slight cavity relaxation suppresses the revival of molecular population and the increase in the magnitude of off-diagonal molecular density matrices during the quiescent region in the amplitude-squeezed field case more significantly than in the coherent field case. These features are shown to be closely related to the difference in the dynamics of Q function distributions between amplitude-squeezed and coherent fields. (C) 2003 American Institute of Physics.