With the development of Internet of Things (IoT), radio electronic equipment has played a vital role in various applications. Furthermore, the non-contact wireless power transmission technology has brought a new round of innovation for the power supply of electronic devices in the IoT. The energy of radio wave and various electromagnetic radiation can become the power source of electronic equipment. By using a rectifier circuit linked to a receiving antenna, this free radio wave energy can be captured and converted into usable a DC voltage for electronic applications. However, for miniaturized electronic equipment, the diodes in the microwave rectifier circuit will produce high-order harmonics, resulting in a large amount of power loss, which decreases the rectification efficiency dramatically. Therefore, it is particularly necessary to design a rectifier circuit that can suppress harmonics. In this paper, a class-F rectifier circuit working at 5.8 GHz is proposed and analyzed. The rectifier circuit can separate the consumption of voltage and current in the diode and realize a high-efficiency rectification. The simulation results show that the rectification efficiency can reach 77.0% at the input power of 16.5 dBm.