Complementary ensemble empirical mode decomposition (CEEMD) can deal with non-stationary random signals very well, but there are still some shortcomings, such as the fitting overshoot/undershoot and end effects problems. A new method for solving the exiting problem that is shape-preserving piecewise cubic spline (SPPCS) CEEMD based on homotopy least squares-support vector double regression (HLS-SVDR) is proposed in this paper, and to achieve correct and efficient EMD decomposition of signals. Firstly, the SPPCS is used to eliminate the fitting overshoot/undershoot problem in the process of structuring the upper and lower envelope curve, and valid envelope curve can be obtained. Then, the HLS-SVDR is introduced to predict and replace the left and right values at both ends of the mean values of the upper and lower envelopes of extreme points of each layer signals for restraining the end effects. Lastly, the proposed method is applied to analyze the case of the feature extraction of rolling bearing’s slight fault. The experimental results indicate that the proposed method can effectively and accurately extract the rolling bearing’s slight fault feature. A complete CEEMD algorithm can keep the original characteristics of CEEMD, and also effectively restrain the fitting overshoot/undershoot and end effects problems.