In this paper, a directive antenna design with a combination of electric-magnetic radiators for an radio frequency identification(RFID) system is presented. To generate a directive antenna radiation pattern, a structure combining a dipole and loop antenna is presented. A reader antenna and tag antenna are proposed for the RFID system. For the reader antenna, the frequency bandwidth defined by $S_{11}$<-10 dB is approximately from 820~990 MHz. The forward and backward gain differences are 1.5~2 dBi. For the tag antenna, the frequency bandwidth is approximately from 860~920 MHz with a maximum gain of 3.58 dBi at 910 MHz. In both cases, directive radiation characteristics are observed.