Two identical Coupled Cavity Linac type (CCL) rebuncher cavities to be integrated in the Medium Energy Beam Transport line (MEBT) of a high intensity linac Accelerator have been studied for matching a 40-mA proton beam accelerated by a 3 MeV Radio-Frequency Quadrupole (RFQ) to a 13 MeV Drift Tube Linac (DTL). The rebuncher operates at 325 MHz, and is designed for β = 0.080. The rebuncher aperture radius is 20 mm required by transverse beam dynamics. It is a single gap structure operating in the TM_010 mode for providing longitudinal beam focusing. The unloaded quality Q0 and the required input power to achieve an effective voltage of 150 kV are 27253 and 20.5 kW, respectively. In this work, we present the RF design studies for the high power rebuncher resonator, as well as the considerations of the tuning scheme and the coupler design.