Electron transport through single linear conjugated molecular wires is investigated by using nonequilibrium Green’s function method combined with density functional theory. The investigated molecule is sandwiched between two gold electrodes via S–Au bonds via three different kinds of terminal connections. One of the connections shows an obviously higher electrical conductance than the others. Several factors have been analyzed. Among them terminal coupling and destructive quantum interference play the main role. A significant structural feature of well conductive conjugated molecules has been pointed out which may provide a quick prediction before time-consuming calculations. Furthermore, we find that the conductance of all the studied molecular wires drops first and then increases with the molecular length increasing. This unusual phenomenon is investigated from the tunneling barrier, shift of molecular levels and electronic coupling between molecule and electrodes, and is ascribed to the competition between two opposite groups of factors.