In this study, a bistable energy harvester (BEH) with a piecewise potential function is proposed to improve its energy harvesting performance. A mathematical model of the piecewise BEH (PWBEH) system is established first and a series of numerical simulation are performed, based on the developed model, in order to investigate the nonlinear dynamic behaviors and energy-harvesting performance of the system. The analysis results for the proposed PWBEH system are compared with a conventional BEH (CBEH). The frequency response results show the stiffness-softening interwell motion of the PWBEH, due to the piecewise potential energy function, which is contrary to the stiffness-hardening behavior of the CBEH. Such softening behavior of interwell motion tends to reduce the operating frequency of the BEH, while significantly increasing the output power. This observation indicate that the introduction of the piecewise potential function to a BEH would be beneficial to the system design for enhancing enegy-harvesting performance at the cost of redundant frequency band, which depends on the characteristics of environmental vibration sources.