A new class of planar filtering quasi-Yagi antenna is presented. It exploits reflectionless-filtering concepts, so that an absorptive branch is incorporated in the antenna to obtain a co-designed filtering functionality. Specifically, a two-order bandstop-filter (BSF) unit and a grounded resistor loaded at its end are combined to form this absorptive branch, which is connected in parallel with the initial planar quasi-Yagi antenna. Thus, by designing the input-power-reflection coefficients of the absorptive branch and the quasi-Yagi antenna to be nearly complementary in frequency, the out-of-band power of the antenna is transmitted by the BSF to be dissipated at its ending resistor. In this manner, a bandpass-filtering operation along with the radiation capability is attained. The simulation results demonstrate that the out-of-band radiation efficiency of the quasi-Yagi antenna is highly suppressed with the absorptive branch, without almost affecting its in-band performance.