The asymmetric transmission of the linearly polarized waves at normal incidence through the lossy anisotropic chiral structure is demonstrated. The proposed chiral metamaterial structure is composed of hi-layered discontinuous cross-wire-strips, and it is utilized in order to realize polarization rotation. Firstly, the theoretical relations between the incident polarization and the polarization rotation are derived using transmission matrices. Secondly, a strong and dynamically asymmetric transmission of linearly polarized electromagnetic wave through the chiral metamaterial has been demonstrated for microwave region, both by simulation and experimentally. The experiment results are in good agreement with the simulation ones. It can be seen from the results that the proposed chiral metamaterial structure can be used to design novel polarization control devices for several frequency regions.