Herein a dual-band wide-angle reflective circular polarization converter, based on a metasurface was developed. The unit cell is composed of a split square ring and a nested square patch. The split square ring plays the role of creating polarization conversion. The square patch is useful for improving the quality of axial ratio. It was verified that the structure could transform the x-polarized incident wave into left-hand circular polarization in the lower frequency band, and to right-hand circular polarization in the higher frequency band. For y-polarized incidence, the transformation has orthogonal modes to that for x-polarized incidence. Moreover, the 3 dB axial ratio takes place in the ranges of 8.42–12.32 GHz and 18.74–29.73 GHz, corresponding to a relative bandwidth of 37.61%, and 45.35%, respectively. In addition, the polarization conversion efficiency is greater than 99% in the ranges of 8.65–11.83 GHz and 19.55–29.36 GHz. Furthermore, for oblique incidence, the axial ratio remains stable, even at 50° incidence, for the lower frequency band. Lastly, a prototype is fabricated and measured for experimental verification. The measured and simulated results were in good agreement. Compared with other designs in the literature, the proposed converter operates with good performance in dual-band, with high-efficiency, and with angular stability.