Despite the combination of nonlinear vibration suppression (VS) and energy harvesting (EH) has received great attention in recent years, the strategy to simultaneously improve the performance in both purposes and extend the operating amplitude range to low-level excitations is still an open issue. To achieve this goal, this paper proposes a tuned bistable nonlinear energy sink (TBNES) to outperform the typical bistable nonlinear energy sink (BNES). The TBNES replaces the fixed magnet that is opposite to the bistable piezoelectric beam (BPB) in the BNES by a tuning piezoelectric beam (TPB) with a movable tip magnet. On one hand, the TPB with a linear viscous damping and a piezoelectric element can improve both VS and EH performances. On the other hand, the tuning effect can dynamically reduce the elastic potential barrier of the BPB, helping it induce the initial snap-through motion and produce the strong targeted energy transfer at low-level excitations, therefore leading to the extension of its operating amplitude range. The electromechanical model and the magnetic force model are derived for both TBNES and BNES based on Hamilton’s principle and the geometrical dipole–dipole method. Parametric studies are conducted to investigate the influences of key system parameters on their VS and EH performances with three defined figure of merits. With the system parameters optimized by the presented dynamic optimization algorithm, the simulation results show that the performance of the TBNES is better than that of the BNES in VS and EH, and its operating range of excitation amplitudes can be successfully extended. The deep mechanisms for these phenomena are discussed from the aspects of 1:1 resonance, induction of nonlinearity, elastic potential energy, etc. Display omitted •Tuned bistable nonlinear energy sink (TBNES) is proposed to outperform typical BNES.•The electromechanical model and the magnetic force model are derived for TBNES/BNES.•Parametric studies are conducted to investigate the influences of system parameters.•An algorithm is presented to optimize the system parameters of TBNES and BNES.•Improved vibration suppression and energy harvesting functions of TBNES are validated.