This paper reports a circularly polarized (CP) rectifying antenna (rectenna) operating at 35 GHz with high microwave-direct current (mw-dc) conversion efficiency. A pair of side-concave patches is used as a CP receiving antenna with a high gain of 10 dB. A low-pass filter (LPF) at the input port of the rectifying circuit is used to suppress the high order harmonics by 19 dB. Both of the antenna and the LPF are simulated by the full wave EM analysis software of HFSS. The rectifying circuit, consist of a LPF, a diode and a DPF, is simulated by using the ADS software. The dc-pass filter (DPF) is designed to block the fundamental frequency and the harmonics from transmitting to the load. A co-simulation method of HFSS and ADS is applied to optimize the rectenna with a high mw-dc conversion efficiency of 81% is obtained.