Electromagnetic band-gap (EBG) structures have unique properties in controlling the propagation of electromagnetic wave and have been applied to a wide range of electromagnetic devices design. In this paper, a double-sided printed dipole (DSPD) array backed by an EBG reflector is proposed for achieving a low-profile design as well as gain enhancement. Simulation results show that a reduction of more than 55% in antenna height can be obtained by placing the DSPD array over an EBG reflector rather than a perfect electric conductor (PEC) reflector. And the obtained gain of the antenna with an EBG reflector is about 1.9 dB higher than that with a PEC reflector at the operating frequency 2.77 GHz. The EBG reflector can be utilized to reduce a cavity-backed antenna height and enhance the antenna radiation efficiency. The design has a good potential application to antenna arrays with more elements in wireless communication.