An accurate battery state-of-health (SOH) monitoring is crucial to guarantee safe and reliable operation of electric vehicles (EVs). In this paper, an incremental capacity analysis (ICA) method for battery SOH estimation is proposed. This uses grey relational analysis in combination with the entropy weight method. First, an interpolation method is employed to obtain incremental capacity (IC) curves. The health indexes are then extracted from the partial IC curves for grey relational analysis, and the entropy weight method is used to evaluate the significance of each health index. The battery SOH is assessed by calculating the grey relational degree between the reference and comparative sequences. Experimental tests are conducted on two battery cells with the same specifications to verify the efficacy of the proposed method. The results show that the maximum estimation error is limited to within 4%, thus proving its effectiveness. •An interpolation method is proposed to fit the incremental capacity curve.•Health performance indicators (HPIs) are extracted from partial incremental capacity curve.•A novel battery state of health estimation method based on partial incremental capacity curve is proposed.•The entropy weight method is employed to evaluate the significance of battery evaluation indexes.•The grey relational analysis is used to indicate the state of health of degradation battery.