In this article, a multiband compact patch antenna and a multiband rectifier circuit is proposed for a rectenna operating at 2.4 GHz and 5.8 GHz for RF energy harvesting and wireless power transmission. A modified inverted F shape antenna is used as the main receiving component of the rectenna. The antenna has a compact size of 35×40 mm2. The proposed antenna has good impedance bandwidth (for S11< -10 dB) values of 230 MHz and 620 MHz at the resonant frequencies 2.4 GHz and 5.8 GHz, respectively. The gain values are 3.6 dB and 3.3 dB at 2.4 GHz and 5.8 GHz, respectively. Furthermore, an efficient dual band rectifier circuit is presented. The rectifier circuit is a single branch and consists of a matching network, voltage doubler circuit and a load. The proposed rectifier circuit is designed on RT-Duroid 5880 substrate and the HSMS2850 diode is used for rectification. The rectifier achieves very good efficiency at both frequencies i.e., 71 % and 51.9 % at 2.4 GHz and 5.8 GHz respectively.