A dual-band linear polarization transformer with diode-like asymmetric transmission using a three-layer composite metamaterial was proposed and investigated numerically. The proposed three-layer composite metamaterial was comprised of two layers of asymmetric split-ring resonators and a sub-wavelength cross structures sandwiched symmetrically between these layers. By introducing the sub-wavelength cross structure into the asymmetric chiral metamaterial, an electromagnetic wave tunneling effect formed for the incident waves. Thus, the transmissions in the composite structures can be strongly modified, one of the two off-diagonal cross-polarized transmission (txy) of the Jones matrix is enhanced while all the others (txx, tyy, and tyx) are suppressed extremely at resonances. This present design for enhancing asymmetric transmission via polarization conversion can be used as many novel devices, such as optical isolators, asymmetric wave splitters, and circulators.