This paper presents a bistable inverted L-shaped piezoelectric beam power generation structure, and its dynamic behaviors and power generation performance are studied by positive and reverse sweep waveform experiments. The piezoelectric beam includes the substructure layer and the piezoelectric layer. The material of the piezoelectric layer is the piezoelectric ceramic transducer (PZT), and the material of the substructure layer is the phosphor brass. The positive and reverse sinusoidal excitation signal is selected. The snap through phenomenon and stiffness characteristic of the system are investigated by experimental results of the positive and reverse sweep waveform. The relationship between dynamic behaviors and electrical behaviors of the system is also studied. Experimental results show that the positive and reverse sweep waveform has a great influence on vibration of the nonlinear system. Due to the hard spring characteristic of the system, the large vibration amplitude is easy to appear in the positive sweep waveform. Dynamic behaviors of the piezoelectric system are related to its electrical behaviors. When dynamic behaviors bifurcate, electrical behaviors bifurcate. These results can be applied to explore the vibration characteristic and the power generation of the nonlinear piezoelectric system.