The numerical simulation is applied to analyze Terahertz (THz) transmission properties of the asymmetrical cross periodic metallic structures, which is based on the finite-difference time-domain (FDTD) method. The results show that there exists the band elimination in the THz transmission spectrum for the cross metallic structures. When we investigate the effect of THz transmission properties caused by the offset and keep the length, width and period of the metallic structures unchanged, the frequency location of the transmission depression moves towards low frequency as increasing the offset of one metallic. By rotating the sample and changing the polarization of THz electric field related to the direction of one metallic, THz transmission of the asymmetrical cross metallic structure is strongly sensitive to the polarization, while the symmetrical cross structure is independent of THz polarization.