Vibration energy harvesting holds the promise of providing autonomous power for low-power electronic devices. To improve the issue of the limited bandwidth of the piezoelectric energy harvester, this work proposes a novel T-shaped beam bistable piezoelectric energy harvester with a moving magnet. The moving magnet can not only provide nonlinear force to adjust bandwidth, but also increase the number of system resonance peaks, which improves the utilization of the magnet, enhancing the adaptability of the vibration energy harvesting device to the environment. Established a mathematical model and validated it through experiments. Some parameters, such as external resistance, magnet spacing, and spring stiffness, are analyzed by theoretical analysis. The results indicate that, at an acceleration amplitude of 0.3 g and a frequency of 15.7 Hz, the peak output power of the main support beam is 2.36 mW. Similarly, at an acceleration amplitude of 0.3 g and a frequency of 15.6 Hz, the peak output power of the parasitic cantilever beam is 0.56 mW, demonstrating its potential to power low-power electronic components. The moving magnet provides an additional resonance peak for the harvester, offering a new method for the design of broadband magnetic nonlinear piezoelectric energy harvesters in the near future.