Piezoelectric energy harvesting technology is a promising strategy for powering wireless sensor networks. However, piezoelectric energy harvesters (PEHs), especially linear PEHs, usually have narrow operating frequency bandwidth. In this study, in order to broaden frequency bandwidth, a nonlinear multi-stable magnetically induced PEH array (MPEHA) with asymmetric potential wells is proposed. Specifically, the proposed MPEHA is consisted of piezoelectric energy harvesting technique, multi-resonance array technique and magnetic force based nonlinear technique. Both theoretical and experimental studies are conducted to investigate the energy performance and to analyze the dynamic characteristics of MPEHA with snap-through motions among the multiple stable positions. As for theoretical study, a mathematic model of the potential function of the proposed harvester is established and the influence of magnetic force on the potential well configuration is quantitively investigated. As for experimental study, experiments including open-circuit voltage experiment and capacitance charging experiment are conducted using MPEHA with three-beam arrays. Our experimental study demonstrates that MPEHA has better performance than the traditional PEHA due to the magnetic coupling effect. Under excitation acceleration of 3 m s−2, the performance of bi-stable MPEHA is improved by 80.2%, compared with PEHA.