Large-size and heavy-load slewing bearings, which are mainly used in heavy equipment, comprise a subgroup of rolling bearings. Owing to the complexity of the structures and working conditions, it is quite challenging to effectively diagnose the combined failure and extract fault features of slewing bearings. In this study, a method was proposed to denoise and classify the combined failure of slewing bearings. First, after removing the mean, the vibration signals were denoised by maximum correlated kurtosis deconvolution. The signals were then decomposed into several intrinsic mode functions (IMFs) by complementary ensemble empirical mode decomposition (CEEMD). Appropriate IMFs were selected based on the correlation coefficient and kurtosis. The approximate entropy values of the selected IMFs were regarded as the characteristic vectors and then inputted into the support vector machine (SVM) based on multiclass classification for training. The practical combined failure signals of the 3 conditions were finally recognized and classified using SVMs. The study also compared the proposed method with 5 other methods to demonstrate the superiority and effectiveness of the proposed method.