Electron transport through molecular bridges connecting nano-scale electrodes is investigated theoretically with the coupling effect of an electron with molecular vibrations in the bridge. The ground state of the bridge molecule changes from a polaron state to an undressed state with the increase of the transfer integral. The electronic excited states in the bridge are also determined. Transition probabilities between these states are estimated by the golden rule including the excitation of molecular vibrations. By solving the master equation with these transition probabilities, we simulate the electron transfer process in the molecular bridge. [DOI: 10.1380/ejssnt.2006.311]