Electron transport properties of molecular junctions formed by 1, 4-dithiolbenzene(DTB) coupled to 1,1,1 Au nanowires are investigated by using the method of non-equilibrium Green's functions based on first-principle density functional theory. Different S-Au contact configurations are constructed and optimized. The junction with tip-type Au electrode top binding to a thio (S) atom is illustrated by the best configuration for electron transport. Juntions with asymmetric electrode-DTB contact show excellent rectifying performance (the largest rectification ratio being 25.6). Other junctions display negative differential resistance (NDR) effect twice. Analysis shows that the rectifying effect may originate from the difference between the stabilities of S-Au contact modes at both sides. Molecular orbitals including the tip Au atoms are calculated. In low bias region, the orbitals near the Fermi energy dominate the electrons transmission; while, as the bias increases, those apart from the Fermi energy contribute to the transport, along with the DTB eigen-level. During the whole process, the locations and amplitude of transmission vary with bias voltage and I/V curves show two peaks, resulting in twice-NDR effect.