Targeting the mode-mixing problem of intrinsic time-scale decomposition (ITD) and the parameter optimization problem of least-square support vector machine (LSSVM), we propose a novel approach based on complete ensemble intrinsic time-scale decomposition (CEITD) and LSSVM optimized by the hybrid differential evolution and particle swarm optimization (HDEPSO) algorithm for the identification of the fault in a diesel engine. The approach consists mainly of three stages. First, to solve the mode-mixing problem of ITD, a novel CEITD method is proposed. Then the CEITD method is used to decompose the nonstationary vibration signal into a set of stationary proper rotation components (PRCs) and a residual signal. Second, three typical types of time-frequency features, namely singular values, PRCs energy and energy entropy, and AR model parameters, are extracted from the first several PRCs and used as the fault feature vectors. Finally, a HDEPSO algorithm is proposed for the parameter optimization of LSSVM, and the fault diagnosis results can be obtained by inputting the fault feature vectors into the HDEPSO-LSSVM classifier. Simulation and experimental results demonstrate that the proposed fault diagnosis approach can overcome the mode-mixing problem of ITD and accurately identify the fault pattes of diesel engines.