In this paper, we investigate the quantum dynamics of the Λ　configuration atom-molecular three-level system analytically and numerically. Then the production rate of molecule is consequently studied. Our results show that the production rate depends on the initial condition. Under ideal condition, one can have complete transformation with the equivalent Rabi frequency when the initial state is the atomic state, while for the dark state, the production rate is constant. The detuning of the coupling optical field usually decreases the production rate, but increases it for the dark state.