The electronics properties for benzene derivatives with different side groups connected to two gold electrodes with symmetric contacts are investigated by using first-principles methods based on the density functional theory. We have found that a bias can induce a transition from the electron-withdrawing behaviors to the electron-denoting behaviors for the OH side group in a phenoldithiol molecule. The degree of asymmetry of the I-V characteristics and the magnitudes in current depend remarkably on the type and number of attached side groups. The detailed analysis illustrates that the "doping" effect of the side groups and the asymmetry of potential profile in devices under different bias polarities are intrinsic origins leading to such observed phenomena. The results show that it is feasible to import some particular characteristics to a benzene-dithiol molecular device through an attachment of different side groups.