In order to optimize the Mel-Frequency Cepstral Coefficient (MFCC) feature extraction algorithm, improve the recognition accuracy of respiratory sound signals, and achieve the purpose of identifying Chronic Obstructive Pulmonary Disease (COPD), a feature extraction algorithm with the fusion of MFCC based on Hilbert-Huang Transform (HHT) and short-term Energy, named HHT-MFCC+Energy, was proposed. Firstly, the preprocessed respiratory sound signal was used to calculate the Hilbert marginal spectrum and marginal spectrum energy through HHT. Secondly, the spectral energy was passed through the Mel filter to obtain the eigenvector, and then the logarithm and discrete cosine transform of the eigenvector were performed to obtain the HHT-MFCC coefficients. Finally, the short-term energy of signal was fused with the HHT-MFCC eigenvector to form a new feature, and the signal was identified by Support Vector Machine (SVM). Three feature extraction algorithms including MFCC, HHT-MFCC and HHT-MFCC+Energy were combined with SVM to recognize the respiratory sound signal. Experimental results show that the proposed feature fusion algorithm has better respiratory sound recognition effect for both COPD patients and healthy people compared with the other two algorithms:the average recognition rate of the proposed algorithm can reach 97.8% on average when extracting 24-dimensional features and selecting 100 training samples, which is 6.9 percentage points and 1.4 percentage points higher than those of MFCC and HHT-MFCC respectively.