Metamaterial of dual-square array is proposed to design a dual-band circular polarizer. The novel design of asymmetric unit cell and layout of duplicate arrays significantly enhances the coupling between electric and magnetic fields. Simulation and measurement results show that the polarizer presents wide angle circular dichroism and circular birefringence. Moreover, the polarization conversion of the proposed metamaterial changes with frequency, incident angle, and polarization of incident waves. The fundamental mechanism behind is concluded to be the angle-dependent chirality and dispersion of our novel design.