In the article, a broadband rectenna is proposed that can harvest energy from low input power levels. A broadband rectenna is designed that can operate between 1.4 GHz and 2.8 GHz with a bandwidth of 1.4 GHz. The proposed rectenna covers two important bands, i.e., GSM 1800 MHz and ISM 2450 MHz. The antenna consists of an antenna and a rectifier. A hexagonal patch antenna is designed with a defective ground structure that can operate from 1.4 GHz to 2.8 GHz. For rectification purposes, the HSMS2850 Schottky diode is used. To achieve good conversion efficiency, a matching circuit (a combination of bandpass and high-pass section) is designed. Maximum simulated conversion efficiencies achieved at 1.8 GHz with a load resistance of 1.3 kΩ are 21%, 36.3%, 51.2%, 63.7%, and 73.4% at power levels of -20 dBm, -15 dBm, -10 dBm, -5 dBm, and 0 dBm, respectively. Simulated conversion efficiency achieved at 2.45 GHz with a load resistance of 2 kΩ is 22.5%, 35%, 46%, 57.2%, and 68.5% at power levels of -20 dBm, -15 dBm, -10 dBm, -5 dBm, and 0 dBm, respectively. With an optimum load of 2 kΩ and IPLs of -20 dBm, -15 dBm, -10 dBm, -5 dBm, and 0 dBm, the measured conversion efficiencies at 1.8 GHz are 22%, 36%, 51.5%, 65%, and 66.4%, respectively, and at 2.45 GHz they are 22%, 36%, 46%, 57%, and 67%, respectively.