In this paper, we first design an antenna array with dual linear polarizations, then a four-layer transmitarray to convert linear polarizations to circular polarizations, which operates in the Ku-band downlink satellite band (10.7 GHz~12.75 GHz, center frequency at 11.7 GHz). Bisected Split- Ring structure was employed in the transmitarray design due to its larger bandwidth in circular polarization axis ratio and lower insertion loss properties. The unit cell of FSS is 0.46 $\lambda\times$ 0.46 $\lambda$, and the incident wave must be incident at $45^{\circ}$ (the angle between E-field of the incident wave and the y-direction) to convert linear polarization to circular polarization. The phase control is approximately 130° in range, the oblique incidence range is approximately 0-20°, and the transmitarray diameter was 124 mm. The measured gain of the dual-polarized antenna array with the transmitarray was about 18.8 dB and 18.6 dB, with the y-polarization waves turning into left-handed circular polarization (LHCP) and the x-polarization waves to right- handed circular polarization (RHCP). The measured 3 dB axis ratio BW ranges from 11.66 to 11.97 GHz. Then we rotated further the original design of the transmitarray by $45^{\circ}$ in z-axis. The dual-polarized array antenna will maintain the original polarization direction through the transmitarray. The measured gain of the transmitarrav prototype is 20.16 dB and 20.16 dB. Our experimental measurements match well with the simulated. With dual illuminations, all four polarizations (V-LP, H-LP, LHCP, and RHCP) can be obtained by simply turning the FSS by $\pm 45^{\circ}$.