The state of health (SoH) of lithium-ion batteries not only directly affects the accuracy of the state of charge estimation, but is also closely related to the safe operation throughout the battery lifecycle. Accurate SoH estimation is therefore a core issue in lithium-ion battery applications. To address the limitations of data-driven SoH estimation methods, such as poor generalization ability and low estimation accuracy, a lithium-ion battery SoH estimation method based on charging curves and an improved Backpropagation (BP) neural network is proposed. First, based on the constant-current charging curves, a health feature termed the time interval for equal charging voltage difference (TI-ECVD) is designed to simulate random constant-current charging segments, thereby simplifying the input parameters of the SoH estimation model. Second, leveraging the simple structural of the BP network, a genetic algorithm (GA) and the Levenberg-Marquardt (LM) algorithm are incorporated to form a GA-LM-BP network. The GA is used to mitigate the risk of the BP network falling into local optima, while the LM algorithm improves its convergence speed. Finally, based on test data from an autonomous experimental platform, a SoH estimation model is constructed. Comparative analysis with similar estimation methods demonstrates that the proposed method achieves superior performance in both estimation accuracy and computational efficiency.