A compact high directive EBG resonator antenna operating in two frequency bands is described. Two major contributions to this compact design are using single layer superstrate and using artificial surface as ground plane. To obtain only the lower operating frequency band using superstrate layer is enough, but to extract the upper operating frequency band both superstrate layer and artificial surface as ground plane are necessary. Therefore, design of a superstrate to work in two frequency bands is very important. Initially, using appropriate frequency selective surface (FSS) structure with square loop elements, we design an optimum superstrate layer for each frequency band separately to achieve maximum directivity. Also, to design an artificial surface to work in the upper frequency band we use a suitable FSS structure over dielectric layer backed by PEC. Next, by using the idea of FSS structure with double square loop elements we propose FSS structure with modified double square loop elements, so that it operates in both of the desired operating frequency bands simultaneously. Finally, the simulation results for two operating frequency bands are shown to have good agreement with measurements.