Abstract: Based on the piezoelectric theory and Euler-Bernoulli beam model, a theoretical model of a cantilever piezoelectric energy harvester is established in this paper. The governing equations and boundary conditions are derived by using the Hamilton's variational principle. Influence of the capacitance is also considered in the model. The general solution of the governing equations is obtained by using the Galerkin method. The output power and output voltage of an energy harvester are analyzed under harmonic vibration of the base. The results show that the capacitance significantly decreases the output power of the energy harvester. Due to the influence of capacitance, the optimum external resistance for maximum output power is 500 kΩ, while the optimum external resistance for maximum voltage is 3 MΩ. Finally, the base excitation frequency should be as close as possible to the natural frequency of an energy harvester; the output power and output voltage reach the maximum value when the base excitation frequency is equal to the natural frequency. The result provides a theoretical basis for the optimal design of piezoelectric energy harvester, which has important research significance and practical value.