Prognostics and health management (PHM) are developed to accurately estimate the state of health (SOH) of lithium-ion batteries, which are crucial parts for planning the employment strategy in energy storage systems. Numerous studies about the data-driven batteries prognostics mostly assume complete and stable charging/discharging data. The on-board prognostics with random charging/discharging behaviors remains a challenging problem. This paper proposes a novel batteries prognostics method using random segments of charging curves, aiming at improving the flexibility and applicability in practical usage. Firstly, partial incremental capacity analysis is conducted within specific voltage range. And the extracted partial incremental capacity curves are used as features for SOH estimation and prognostics. Second, a long short-term memory network guided by Bayesian optimization is proposed to automatically tune the hyper-parameters and achieve accurate SOH estimation results. The effectiveness and robustness of the partial incremental capacity features acquired from different voltage ranges are investigated to provide guidelines for users. The superiority of the proposed method is validated on lithium-ion battery aging datasets from NASA and CALCE Prognostics Data Repository. The experimental results show that it can accurately predict aging patterns and estimate SOH by solely using small segments of charging curves, showing a promising prospect. •Propose a novel battery prognostic method with LSTM and partial IC features.•Presented partial IC features avoid the identification of specified IC curve peaks.•Bayesian optimization is adapted into LSTM to automatically tune hyper-parameters.•The effectiveness is comprehensively investigated in two battery aging datasets.