A vibration-based energy harvester and its equivalent circuit models have been reported. Most models predict voltage signals at harmonic excitation. However, vibrations in a natural environment are unpredictable in frequency and amplitude. In this paper, we propose a realistic equivalent circuit model of a frequency-up-converting impact-based piezoelectric energy harvester. It can describe the behavior of the harvester in a real environment where the frequency and the amplitude of the excitation vary arbitrarily. The simulation results of the model were compared with experimental data and showed good agreement. The proposed model can predict both the impact response and long term response in a non-harmonic excitation. The model is also very useful to analyze the performance of energy conversion circuitry with the harvester.