Generally, the State-of-Health (SOH) monitoring and Remaining Useful Life (RUL) prediction and assessment of lithium-ion (Li-ion) batteries need to use sensors to obtain the degradation test data of the same type of batteries and establish the degradation model for reference. However, when the battery type is unknown, a usable reference model cannot be obtained, so its prediction and evaluation may be relatively inconvenient. In this paper, the State of-Health prediction for lithium-ion batteries based on a novel hybrid scheme is proposed. Firstly, historical charge/discharge time series and capacity series are extracted to analyze and construct Health Indicators, then using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to decompose the Health Indicator series into the trend and non-trend terms. Among them, the relatively smooth trend item data series uses the Autoregressive Integrated Moving Average model (ARIMA) for prediction; when dealing with the data series of non-trend items which are obviously non-smooth and seemingly random, the residuals predicted by ARIMA and the non-trend items obtained by CEEMDAN decomposition are combined into new non-trend items; then the least square support vector machine (LSSVM) is introduced to build a nonlinear prediction model and make predictions. Finally, combining the prediction results of the trend item data series and the non-trend item data series as a reference for the assessment of the state of health and remaining useful life. The 13 experimental results of 3 batteries verify the effectiveness of the scheme.