In this paper, the working mechanism of a wideband absorber designed with an adjustable and highly selective notch band is studied, in which the narrow notch band is independently controlled by the lower lossless layer of the absorber, while the upper lossy layer loaded with lumped resistors realizes absorption. We present two instances with geometrically controlled and electrically controlled notch bands, respectively. Without decreasing absorption performance, the notch position can be flexibly adjusted throughout the entire frequency band by simply modifying the dimension of the lossless frequency-selective surface (FSS) or changing the capacitance of the varactor, i.e., using geometric control or electrical control. The narrow notch band allows two wide absorption bands to be retained on both sides; therefore, good stealth performance is still guaranteed. Equivalent circuit models (ECM) are proposed to further explain the principle. The frequency-domain simulation, ECM, time-domain simulation, and experimental results are in good agreement and validate the adjustability and high selectivity of the notched absorbers. At the end of this paper, an FSA-backed monopole antenna is simulated and measured, which clearly illustrates that these FSAs can serve as the ground plane for antennas and realize out-of-band RCS reduction.