Using a spatially symmetric phenyldithiolate molecule sandwiched between two gold electrodes as model system and through shifting one electrode from symmetric contact site to form asymmetric contact, we investigated the properties of electronic transport in such a device by the first-principles. It was found that the I(G )-V characteristics of a device show significant asymmetry and the magnitudes of current and conductance depend remarkably on the variation of molecule-metal distance at one of the two contacts. Namely, an asymmetric contact would lead to the weak rectifying effects on the current-voltage characteristics of a molecular device. The analysis shows that the HOMO is responsible for the resonant tunneling and its shift due to the charging of the device while the bias voltage is the intrinsic origin of asymmetric I(G)-V characteristics.