Based on the structural characteristics of a molecular wire coupled to electrodes，the electronic tunneling process in a molecular device consisting of such a composite molecule under a bias is modeled by a simplified successive tunneling model with asymmetric multiple potential barriers in series. An analytical expression for the electronic transmission spectrum is obtained. Then，the relations between the transmission coefficient and various parameters，such as the width and height of the barrier，the distance between two neighboring barriers，the effective mass of electron, and the bias voltage, are calculated. It is found that when the electron energies are equal to some special values，obvious resonant tunneling occurs，and the transmission coefficient is very sensitive to the parameters mentioned above. The results presented here suggest that the transport behaviors of molecular electronic devices can be significantly modified in a controlled way, for example，by altering the constituents or/and the configurations of the composite molecule.