In this paper, a design scheme for a dual‐band waveform‐selective metasurface absorber (MSA) is presented based on the combination of two metal resonator structures loaded with nonlinear circuits. Dual‐band MSAs with four different configurations are constructed by loading capacitor/inductor‐based nonlinear circuits into the gaps of two square‐patch (SP) and two square‐ring (SR) resonators, all of which can achieve selective absorption of short pulses and continuous waves (CWs) at two frequencies independently. As a typical example, the dual‐band MSA with the SP resonator loaded with the inductor‐based nonlinear circuit and the SR resonator loaded with the capacitor‐based nonlinear circuit is systematically studied. First, the selective absorption performance of the dual‐band MSA for CWs and pulses under different input powers is demonstrated. Second, the selective absorption properties of the dual‐band MSA for pulses with different pulse widths are studied. Third, the waveform‐selective absorption characteristics of the dual‐band MSA for oblique TE and TM waves are also illustrated. Finally, the influence of circuit component parameters on the selective absorption properties of pulses and CWs is systematically studied. The proposed dual‐band MSAs have potential application areas such as antenna design, wireless communications, and electromagnetic compatibility.