Supercapacitors have the advantages of fast charging and discharging, high power density, and long life, which are widely used in energy storage systems for new energy vehicles. Reliable operation of the system requires the acquisition of its remaining electricity, which is to estimate its state of charge (SOC). Relying on the equivalent analog circuit model of a single supercapacitor, this paper establishes a state-space model of the capacitor second-order nonlinear system with the multi-capacitor terminal voltage in the model as the state, the capacitor input current as the control input, and the capacitor output voltage as the observation output, and contains the leakage current caused by the self-discharge phenomenon. In order to improve the simulation accuracy, different model parameters were identified to characterize the charging and discharging conditions. In this paper, a nonlinear observer algorithm is used to obtain the internal state of the model to realize the estimation of SOC. The results of the charging and discharging experiment show that considering the leakage factor and establishing the charging and discharging model with different parameters, the dynamic characteristics of the supercapacitor can be better simulated, and the nonlinear observer algorithm has a stable tracking ability.