We study bosonic atoms trapped in a triple-well with synthetic gauge field. The energy spectrum of the system can be tuned by an effective magnetic field. For a non-interacting system, eigen-states with different momenta will be the ground state with the magnetic field varying. In the full quantum scheme, we find the critical ratio between the tunneling and interaction strength for localization of system under the repulsive interaction. We also discuss the macro-rotation effect induced by the magnetic field and the boundary effect of the temporal evolution for a non-interacting system.