Lithium-ion capacitor is a hybrid electrochemical energy storage device which combines the merits of lithium-ion battery and electric double-layer capacitor. The precise state of charge estimation is essential to utilize lithium-ion capacitor efficiently. In this paper, the electrical characteristics of lithium-ion capacitor have been studied and the corresponding equivalent circuit model is established. Then, an adaptive square root cubature Kalman filter with variable forgetting factor recursive least square has been proposed to achieve state of charge estimation at each sampling step. The proposed method identifies the model parameters and noise statistics in real time, leading to obtain accurate SOC estimation even if the method is initialized with inaccurate parameters. Estimations under four working conditions are quantitatively studied, the experimental results show that the proposed method has better performance and the corresponding maximum root mean square error is controlled within 1%. Furthermore, the verification of robustness illustrates that the proposed method remains stability and acceptable accuracy when external interference and inaccurate initial SOC are included.