Selective wave-transmitting absorbers which have one or more narrow transmission bands inside a wide absorption band are often demanded in wireless communication and radome applications for reducing the coupling between different systems, improving anti-jamming capability, and reducing antennas’ radar cross section. Here we propose a feasible method that utilizing composite of two metasurfaces with different polarization dependent characteristics, one works as electromagnetic polarization rotator and the other as a wideband polarization dependent electromagnetic wave absorber. The polarization rotator produces a cross polarization output in the wave-transmitting band, while preserves the polarization of the incidence outside the band. The metasurface absorber works for certain linear polarization with a much wider absorption band covering the wave-transmitting frequency. When combining these two metasurfaces properly, the whole structure behaves as a wideband absorber with a certain frequency transmission window. The proposal may be applied in radome designs to reduce the radar cross section of antenna or improving the electromagnetic compatibility in communication devices.