In this paper, a circular polarization selective surface (CPSS) with high angular stability is proposed to realize reflectarray antenna with high gain and left-handed circular polarization (LHCP) characteristics. Meanwhile, the proposed CPSS is nearly transparent for the incidence of righthanded circular polarization (RHCP) wave, which can be used as a radome for a RHCP antenna. For the design of LHCP reflectarray antenna, the conventional array theory is utilized to predict the antenna performance, whose results are then compared with the full-wave simulations. The simulated maximum gain of the reflectarray antenna is 19.5 dB and the simulated axial ratio is below 0.6dB within the 3-dB gain bandwidth of 15.6%. For the application of RHCP radome, the CPSS can maintain the performance of a RHCP feed antenna operating in the same frequency band of the LHCP reflectarray antenna.