A dual band microstrip patch antenna integrated with pinwheel-shaped electromagnetic band-gap (EBG) structures is proposed. The patch antenna consists of a pair of spiral slots on the patch and is fed by using coaxial line. Its full-wave simulation predicts dual bands from 4.43 GHz to 4.56 GHz and from 4.96 GHz to 5.1 GHz in the C-band. The designed EBG with eight pinwheelshaped slots addresses smaller frequency drift compared with the traditional square mushroom-like EBG when applied to the patch antenna. With the help of designed EBG structure, the impedance bandwidth, radiation efficiency, and gain of the patch antenna are improved significantly. The 10 dB impedance bandwidth is extended by 3.4% and 6.5% at the low-and high-frequency bands, respectively. The radiation efficiency is increased by 5% and 17.8%, and the realized gain is enhanced by 1.87 dB and 1.56 dB at 4.57 GHz and 5.06 GHz, respectively. The designed EBG structure may have many applications in other types of planar antennas.