As a basic functional unit of molecular electronics, the structure of single molecule sandwiched between nano-electrodes has attracted a lot of interest in molecular science, in particular, its current-voltage (I-V) characteristic induced by an external field. Aiming at the molecular nano-junction which is composed of lead/molecule/lead, we use the method of extended master equation to compute the steady and transient current in the molecular nano-junction under the action of an externally applied electric field. The current can be adjusted by the external field, the relaxation in the molecule, the intra-molecular vibrational energy redistribution, etc. Owing to the strong electronic-vibrational coupling, the I-V curve has an inelastic characteristic in the molecular nano-junction and the stable current increases stepwise with the applied bias voltage increasing. The Franck-Condon blockage can be effectively removed by the external field. The molecular nano-junction being excited by different-width Gaussian pulses, the currents in the molecular nano-junction take different times to reach their steady state. The pulse width has a strong effect on the transient current enhancement. The transient current appears obviously for the 1 ps width pulse excitation. In this case the molecule is at a non-equilibrium state and the currents at both ends of the molecule are different. With the pulse width and the applied voltage increasing, the current through the molecular nano-junction tends to be balanced.