We propose a polarization-twisting metasurface antenna (PTMA) to generate the dual-band dual-circularly polarized (CP) radiation by integrating a dual-linear-to-circular polarization converter (DLCPC) with a linear polarization conversion metasurface (LPCM) in the Ku-band. The DLCPC possesses the functionality of polarization selection and is capable of transforming the linearly polarized (LP) waves into right hand CP (RHCP) waves in low-frequency (LF) and left hand CP (LHCP) waves in high frequency (HF). Based on the DLCPC, the dual-band dual-CP PTMA is designed and fabricated, and then, the measured results indicate that the PTMA is capable of realizing the RHCP radiation in LF and the LHCP radiation in HF. In the meanwhile, the common bandwidths of −1.5 dB gains and 3 dB axial ratios are 12.25–12.95 and 14.00–14.55 GHz, respectively. Our design, by integrating the DLCPC and LPCM to construct the dual-band dual-CP PTMA, should, thus, pave the way for building up more efficient wireless communication systems with the requirement of different CPs as the receiver and the transmitter at downlink and uplink in the Ku-band.