An asymmetric chiral metamaterial structure is constructed by using four double-layered U-shaped split ring resonators, which are each rotated by 90° with respect to their neighbors. The peculiarity of the suggested design is that the sizes of the electrically and magnetically excited rings are different, which allows for equalizing the orthogonal components of the electric field at the output interface with a 90° phase difference when the periodic structure is illuminated by an x-polarized wave. As a result, left-hand circular polarization and right-hand circular polarization are obtained in transmission at 5:1 GHz and 6:4 GHz, respectively. The experiment results are in good agreement with the numerical results.