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A dual-band antenna for the reader of the Radio Frequency Identification (RFID) applications is proposed. The antenna design to achieve the dual-frequency band is carried out by using the annular plate with curved and rectangular slots. The simulation is done by using CST based on the Finite Integral Method. Furthermore, the parameters of antenna are optimized with the Quasi Newton method. The effects of antenna parameters are analyzed. Along the UHF-RFID band, the pattern is unidirectional beam. The half-power beamwidths in xz- and yz- planes are 78 and 64 degrees, respectively. The bandwidth covers 911-925.6 MHz. The directivity is 8.33 dBi. For 2.45 GHz band, the pattern is also unidirectional beam. The half-power beamwidths in xz- and yz-planes are 58 and 21 degrees, respectively. The bandwidth covers 2.32-2.52 GHz. The gain is 9-10.5 dBi.