Using the density-functional theory and the non-equilibrium Greens function method, we investigate the electronic transport properties and rectifying performances of four different molecular devices based on different end groups from the same D-B-A molecule. The results show that the end groups can significantly affect the rectifying performances of such molecular rectifiers, because the end groups can influence the coupling effects between the molecule and the electrodes, thus changing the delocalization of molecular orbitals, and further changing their transport properties and rectifying performances. More interestingly, it is found that the rectifying directions and working mechanism for all of our studied systems are in disagreement with ones proposed originally by Aviram and Ratner. This property can be rationalized through the asymmetric shift of molecular levels under biases of different polarities.