Lithium-ion batteries (LIBs) are utilized as a major energy source in various fields because of their high energy density and long lifespan. During repeated charging and discharging, the degradation of LIBs, which reduces their maximum power output and operating time, is a pivotal issue. This degradation can affect not only battery performance but also safety of the system. Therefore, it is essential to accurately estimate the state-of-health (SOH) of the battery in real time. To address this problem, we propose a fast SOH estimation method that utilizes the sparse model identification algorithm (SINDy) for nonlinear dynamics. SINDy can discover the governing equations of target systems with low data assuming that few functions have the dominant characteristic of the system. To decide the state of degradation model, correlation analysis is suggested. Using SINDy and correlation analysis, we can obtain the data-driven SOH model to improve the interpretability of the system. To validate the feasibility of the proposed method, the estimation performance of the SOH and the computation time are evaluated by comparing it with various machine learning algorithms.