The nonlinear energy pumping in a two-degree-of-freedom system comprising a damped linear oscillator coupled to cubic damping absorber is studied. It is verified that the nonlinear pumping energy can be performed by cubic damping absorber besides cubic stiffness absorber. The resonance capture is verified by time-frequency analysis (Hilbert Transform). The energy pumping efficiency is put forward for quantitative analysis, and the optimal parameters of system are obtained. The amplitude of main oscillator can be attenuated in a very short duration. The result may be significative for engineering implementation.