The study focuses on the design of an energy harvesting nonlinear dynamic vibration absorber (DVA) for possible vibration attenuation and energy generation. As an application vibration mitigation of a base-excited single degree of freedom (SDOF) system is considered. Conventional DVAs are widely used as vibration control devices that undergo large displacements in order to dissipate the energy from the primary structure. For an energy harvester higher the vibration higher is the energy generated. Therefore, if an energy harvester is attached to the DVA, the primary structure DVA interaction can be used for dual purposes. In this study, a duffing-type nonlinear DVA system with a piezo patch is proposed as energy harvesting nonlinear DVA to mitigate the vibration and to obtain electricity. The modeling of the total system is carried out considering the electromechanical interactions between the harvester-DVA and structural system. The formulation is done in time domain and a simulation study is carried out for harmonic base excitation to understand the effect of nonlinearity in voltage generation. A frequency sweep study is carried out to locate the frequency band in which the system responses are consistently higher. Further, the important design parameters are identified. A parametric study to obtain optimal design parameters is also reported. The advantages of nonlinear energy harvesting DVA over the linear ones are many. A nonlinear harvester provides power over a broad range of frequencies and, therefore would be able to dissipate energy from the primary structure over wideband excitations. Finally, the performance of the designed nonlinear DVA system with harvester is examined for vibration mitigation of SDOF primary system. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.