This paper presents a design method of filtering antennas with wide matching bands to realize the integration of multiple functions such as absorbing, filtering, and radiating, and protect the system as well. In our design, an absorptive stub is employed to absorb the out-of-band signals. As such, a cascaded topology with lossy stubs, lossless stubs, and the resonant antenna is proposed to acquire the absorptive filtering antenna. The characteristic of the absorptive stub, and the response of the equivalent circuit are specifically analyzed here. Finally, an absorptive filtering slot antenna is implemented to prove that the method can be used to achieve a matching bandwidth far beyond that of a conventional resonant antenna.