The 3-GeV rapid cycling synchrotron (RCS) of the Japan Proton Accelerator Research Complex (J-PARC) is a high-power pulsed proton driver aiming at 1 MW output beam power. The RCS was beam commissioned in October 2007 and made available for user operation in December 2008 with an output beam power of 4 kW. Since then, the output beam power of the RCS has been steadily increasing following progressions in beam tuning and hardware improvements. So far, the RCS has successfully achieved high-intensity beam trials of up to 420 kW at a low-level intensity loss of less than 1%, and the output beam power for the routine user program has been increased to 210 kW. The most important issues in increasing the output beam power are the control and minimization of beam loss to maintain machine activation within the permissible level. This paper presents the current status of the RCS beam power ramp-up, with particular emphasis on our approach to beam loss issues. The future prospects of RCS beam commissioning and operation are also described.