In this paper, on the basis of tight-binding model and a generalized Green- function method as well as Lanczos algorithm procedure, the effects of the metal-molecule coupling(MMC) strength on the electronic transmission through a metal-single molecule-metal(MMM) system is investigated. Using the Landauer formalism we study some of the significant conductance properties of this system as a molecular wire. Our results show that with the increase of the length of the molecule, the conductance of the molecular wire decreases exponentially. With trans-polyacetylene (trans-PA) as the molecule, we calculate a characteristic time for electron transmission through the MMM system. This time scale measures the delay caused by tunneling through the MMC. Our calculations show that the conductance is sensitive to the MMC strength. The focus is on the significant relationship between this time scale and the strength of the metal-molecule(trans-PA) coupling.