The characteristics of quantum transmission through a four-terminal nano-molecular bridge are investigated theoretically by using tight-binding approach, based on the Green's function with only a π orbital per carbon atom at the site. The transmission probabilities of the electrons transported through the molecular bridge to every terminal are obtained. The electronic current distributions inside the molecular bridge are calculated and shown in graphical analogy by the current density method and Fisher-Lee formulism at the energy points E=±12 and E=±149 where transmission probabilities show peaks, the maximum bond currents are also presented. It is found that the loop currents in molecules are induced by the phase difference of the molecular orbitals.