This paper presents a novel broadband rectenna for ambient wireless energy harvesting over the frequency band from 1.8 to 2.5 GHz. First of all, the characteristics of the ambient radio-frequency energy are studied. The results are then used to aid the design of a new rectenna. A novel two-branch impedance matching circuit is introduced to enhance the performance and efficiency of the rectenna at a relatively low ambient input power level. A novel broadband dual-polarized cross-dipole antenna is proposed which has embedded harmonic rejection property and can reject the second and third harmonics to further improve the rectenna efficiency. The measured power sensitivity of this design is down to -35 dBm and the conversion efficiency reaches 55% when the input power to the rectifier is -10 dBm. It is demonstrated that the output power from the proposed rectenna is higher than the other published designs with a similar antenna size under the same ambient condition. The proposed broadband rectenna could be used to power many low-power electronic devices and sensors and found a range of potential applications.