We know that the RF-DC conversion efficiency of rectenna is strictly affected by the load and the input power. This study proposes a RF-DC-DC circuit, consisting of a rectifying circuit and a DC-DC converter, to improve the efficiency-load characteristic of rectenna. The proposed DC-DC converter can work with constant input impedance independent of the load resistance. Especially, the control part of DC-DC converter is self-powered rather than additional DC power source. We measured the designed RF-DC-DC circuit with a 2.45 GHz microwave power of 80 mW. The conversion efficiency of the rectifying circuit alone is constant over 80% in the load range from 200 Omega to 5000 Omega, when it is connected with the DC-DC converter. Furthermore, the overall efficiency of the RF-DC-DC circuit is almost constant over 66% in this wide load range.