The lithium-ion battery has become the main power source of many electronic devices, it is necessary to know its state-of-health and remaining useful life to ensure the reliability of electronic device. In this paper, a novel hybrid method with the thought of error-correction is proposed to predict the remaining useful life of lithium-ion battery, which fuses the algorithms of unscented Kalman filter, complete ensemble empirical mode decomposition (CEEMD) and relevance vector machine. Firstly, the unscented Kalman filter algorithm is adopted to obtain a prognostic result based on an estimated model and produce a raw error series. Secondly, a new error series is constructed by analyzing the decomposition results of the raw error series obtained by CEEMD method. Finally, the new error series is utilized by relevance vector machine regression model to predict the prognostic error which is adopted to correct the prognostic result obtained by unscented Kalman filter. Remaining useful life prediction experiments for batteries with different rated capacities and discharging currents are performed to show the high reliability of the proposed hybrid method.