Crude oil, as one of the most important energy sources in the world, plays a crucial role in global economic events. An accurate prediction for crude oil price is an interesting and challenging task for enterprises, governments, investors, and researchers. To cope with this issue, in this paper, we proposed a method integrating ensemble empirical mode decomposition (EEMD), adaptive particle swarm optimization (APSO), and relevance vector machine (RVM)—namely, EEMD-APSO-RVM—to predict crude oil price based on the “decomposition and ensemble” framework. Specifically, the raw time series of crude oil price were firstly decomposed into several intrinsic mode functions (IMFs) and one residue by EEMD. Then, RVM with combined kernels was applied to predict target value for the residue and each IMF individually. To improve the prediction performance of each component, an extended particle swarm optimization (PSO) was utilized to simultaneously optimize the weights and parameters of single kernels for the combined kernel of RVM. Finally, simple addition was used to aggregate all the predicted results of components into an ensemble result as the final result. Extensive experiments were conducted on the crude oil spot price of the West Texas Intermediate (WTI) to illustrate and evaluate the proposed method. The experimental results are superior to those by several state-of-the-art benchmark methods in terms of root mean squared error (RMSE), mean absolute percent error (MAPE), and directional statistic (Dstat), showing that the proposed EEMD-APSO-RVM is promising for forecasting crude oil price.