In this paper, a dual-band dipole antenna for passive radio frequency identification (RFID) tag application at 2.45 GHz and 5.8 GHz is designed and optimized using HFSS 13. The proposed antenna is composed of a bent microstrip patch and a coupled rectangular microstrip patch. The optimal results of this antenna are obtained by sweeping antenna parameters. Its return losses reach to -18.7732 dB and -18.2514 dB at 2.45 GHz and 5.8 GHz, respectively. The bandwidths (Return loss <=-10 dB) are 2.42~2.50 GHz and 5.77~5.82 GHz. And the relative bandwidths are 3.3% and 0.9%. It shows good impedance, gain, and radiation characteristics for both bands of interest. Besides, the input impedance of the proposed antenna may be tuned flexibly to conjugate-match to that of the IC chip.