Purpose <p>Due to the priority of small damping, magnetic rolling pendulum (MRP) system has been utilized in the area of energy harvesting, and numerous studies focused on the broadband response characteristic and practical applications of the harvesters. By combining the magnetic force and gravity of the rolling magnet, bistable configurations can be achieved, and the complex nonlinear dynamics under parametric excitation remain an open issue. Therefore, this paper investigate the complex dynamic behaviors of a gravity-induced bistable MRP harvester under parametric excitation.</p> Methods <p>By establishing the dynamic model, the outcomes of the harvester are predicted through electromagnetic induction and finite element analysis. Under sweep and constant frequency excitation, numerical simulations are undertaken to study the dynamics of the system. In addition, the multiple solution characteristics are considered through the basins of attraction.</p> Results <p>Under sweep frequency excitation with a level of 0.3&#xa0;g, the system could oscillate across the potential barrier over a wide range of low frequencies from 4.36&#xa0;Hz to 14.13&#xa0;Hz. Regarding the constant frequency excitations, bifurcation diagrams, and cloud maps of mean square voltage and 0–1 test demonstrate that the system exhibits complex dynamic behaviors including multiple patterns of interwell and intrawell oscillations, and these can be identified by the means of phase orbit, Poincaré map, multiscale entropy, and reconstructed phase-space. Additionally, the multi-solution phenomena of the system reveal that the number of solutions is closely related to the excitation amplitude and frequency.</p> Conclusion <p>In general, this study offers a novel strategy for realizing multistable oscillation, and the optimization and experimental verification of the harvester for enabling low-power consumption devices will be considered in future studies.</p>