High maintenance costs and safety risks due to lithium-ion battery degeneration have significantly and seriously restricted the application potential of batteries. Thus, this paper proposes an efficient calculation approach for state of health (SOH) estimation in lithium-ion batteries that can be implemented in battery management system (BMS) hardware. First, from the variables of the charge profile, only the complete voltage data is taken as the input to represent the complete aging characteristics of the batteries while limiting the computational complexity. Then, this paper combines the light gradient boosting machine (LightGBM) and weighted quantile regression (WQR) methods to learn a nonlinear mapping between the measurable characteristics and the SOH. A confidence interval is applied to quantify the uncertainty of the SOH estimate, and the model is called LightGBM-WQR. Finally, two public datasets are employed to verify the proposed approach. The proposed LightGBM-WQR model achieves high accuracy in its SOH estimation, and the average absolute error (MAE) of all cells is limited to 1.57%. In addition, the average computation time of the model is less than 0.8 ms for ten runs. This work shows that the model is effective and rapid in its SOH estimation. The SOH estimation model has also been tested on the edge computing module as a possible innovation to replace the BMS bearer computing function, which provides tentative solutions for online practical applications such as energy storage systems and electric vehicles.