The state of health (SOH) is an important index for battery management system, and accurate SOH estimation is of great significance for ensuring safe and stable operation of battery. Extracting reliable and effective health features to describe the aging state of battery and constructing accurate and stable estimation model are the main problems we face at present. In order to improve the accuracy of SOH estimation, a fuzzy entropy and particle filter (PF) based SOH estimation method for lithium-ion battery is proposed. Firstly, the fuzzy entropy value is extracted as the aging characteristic of the battery by analyzing the discharge voltage data during the aging process. Secondly, a non-parametric state-space model to describe the aging characteristics of lithium-ion battery is constructed based on the metabolic grey model (MGM) and the temporal convolutional network (TCN). Finally, the closed-loop SOH estimation of lithium-ion battery is realized by PF. In addition, the proposed SOH estimation method is validated using the NASA lithium-ion battery datasets and compared with other methods in the field. The results show that the maximum estimation error of the proposed method is about 5%, the estimation accuracy is improved by about 50% compared with similar methods, and the proposed method exhibits good robustness under different training cycles, which verifies the feasibility and superiority of the proposed method.