The work aims to analyze the effect of damping ratio, frequency, nonlinear coefficient, elasticity coefficient and excitation amplitude on the vibration response characteristics, with the vibration energy harvester as the research object of the vibration pickup structure. First, the physical system model of the vibration pickup structure and the dynamic equation were established, and the theoretical calculation was conducted. Then, homotopy analysis method (HAM) was used to calculate and analyze its response characteristics, so as to obtain the theoretical calculations. Finally, MATLAB was adopted to draw the basic curve of vibration characteristics, so as to obtain the simulated analysis results. Nonlinear coefficient had little effect on the vibration response characteristics. The response amplitude could be increased by reducing the elasticity coefficient, increasing the damping ratio, and controlling the system frequency and excitation amplitude. This will provide a theoretical basis for optimization design of vibration energy harvester’s vibration pickup structure.