Based on the density-functional theory and the non-equilibrium Greens function method, a theoretical study of the electron transport for the systems consisting of the terphenyl molecule connected to two Au electrodes through end-group S (Se) is carried out. The results show that these systems have good rectifying performance and the maximum rectification ratio may reach approximately 6 at a bias of 2.8 V. The rectifying behavior is reduced significantly when one of the two S(Se) atoms located at right end of the molecule is replaced by H. The asymmetric coupling between the molecule and the metal interface leads to different spatial distributions of the MPSH and different shifts of molecular orbital energy levels under positive and negative biases, which is the mechanism of rectifying performance. The systems with S end-groups have obvious rectifying performance because the interaction between S and Au electrode is stronger than that between Se and Au electrode.