It is important to control the magnet current for a high-intensity proton beam because the magnetic field error displaces the beam parameters (i.e., center of orbit, transverse tune, etc.) from the ideal values and such displacements cause severe beam loss. This issue is much more severe for synchrotrons because the magnetic field must be changed for acceleration. For more precise control of the power supplies, we developed low-noise 24-bit A/D boards for high-precision current measurement. In addition, we developed an algorithm and DSP boards to correct the current deviation. We successfully controlled the magnet current at a level of ppm for all frequencies using sextupole magnets in the J-PARC MR. In this paper, the details of the control system and results of the tests using the magnets in the synchrotron are described.