We discuss the relationship between exteal magnetic field and persistent currents of three mesoscopic-coupled rings with charge discreteness. Through numerical calculation and analysis, it is found that the properties of the persistent currents depend on both exteal magnetic flux and coupled factors. The positive coupling between the rings will decrease the persistent currents when 0 ＜ m ＜ 1 with m being the coupling coefficient. The quantum current magnification effect appearing in the rings is also investigated.