The quantum transmission characteristic of three-terminal C60 molecular bridge is investigated theoretically by using Green's function approach based on tight-binding theory with only one π orbital per carbon atom inside C60 molecule. The transmission spectra that electrons transport through the C60 molecular bridge from one terminal to the other two terminals are obtained. The electronic current distributions inside the molecular bridge are calculated and shown in graphical analogy by the current density method based on Fisher-Lee formula at the energy points E=±0.42, ±1.06 and ±1.5, respectively, where the transmission probabilities appear peaks. We found that the transmission spectra are related to the incident electronic energy, and depend on C60 molecular levels strongly. We also found that the electrons transport through the C60 molecular bridge symmetrically, and the multi-point switching properties depend on the energy. That the current distributions in the C60 molecular bridge agree well with Kirchhoff quantum current momentum conservation law is shown.