In this paper, a dual-band dual-circularly polarized antenna array working at Ka-band and K-band based on gap waveguide (GW) technology is proposed. The antenna is composed of a high frequency layer working at Ka-band, a low frequency layer working at K-band, and a grid layer which lowers the far field side lobe level. The power distribution network is formed by the combination of the groove gap waveguide (GGW) and the ridge gap waveguide (RGW). The energy enters the radiation cavity at the same amplitude and phase though this power distribution network. By placing inclined blocks in the cylindrical radiation cavity, the antenna radiates right-handed circularly polarized (RHCP) waves at high frequency with a gain of 14.5dB and left-handed circularly polarized (LHCP) waves at low frequency with a gain of 13.8dB. The simulation results show that the antenna has a wide impedance bandwidth (27.6GHz-29.74GHz at Ka-band, 17.49GHz-21.81GHz at K-band) and a wide axial ratio (AR) bandwidth (27.5GHz-29GHz at Ka-band, 19.2GHz-20.4GHz at K-band). The proposed antenna has the characteristics of high gain, high efficiency, large power capacity, wide operating frequency band, and no need of interlayer welding.