Precise estimation of state of health (SOH) are of great importance for proper operation of lithium-ion batteries equipped in electric vehicles. For real applications, it is however difficult to estimate battery SOH due to stochastic operation, which in turn speeds up aging process of the battery. To attain the precise SOH estimation, an efficient estimation manner based on machine learning is proposed in this study. Firstly, the voltage profile during charging and discharging process and incremental capacity variation are acquired through the cycle life test, and the healthy features correlating to battery degradation are extracted. Secondly, the grey relation analysis and entropy weight method are employed to analyze the healthy features. Finally, the long short-term memory is established to achieve the SOH estimation of battery. The experimental results highlight that the proposed method can effectively predict the battery SOH with preferable accuracy, stability and robustness.