Objective: Heart sounds can reflect detrimental changes in cardiac mechanical activity that are common pathological characteristics of chronic heart failure (CHF). The ACC/AHA heart failure (HF) stage classification is essential for clinical decision-making and the management of CHF. Herein, a machine learning model that makes use of multi-scale and multi-domain heart sound features was proposed to provide an objective aid for ACC/AHA HF stage classification. Approach: A dataset containing phonocardiogram (PCG) signals from 275 subjects was obtained from two medical institutions and used in this study. Complementary ensemble empirical mode decomposition and tunable-Q wavelet transform were used to construct self-adaptive sub-sequences and multi-level sub-band signals for PCG signals. Time-domain, frequency-domain and nonlinear feature extraction were then applied to the original PCG signal, heart sound sub-sequences and sub-band signals to construct multi-scale and multi-domain heart sound features. The features selected via the least absolute shrinkage and selection operator were fed into a machine learning classifier for ACC/AHA HF stage classification. Finally, mainstream machine learning classifiers, including least-squares support vector machine (LS-SVM), deep belief network (DBN) and random forest (RF), were compared to determine the optimal model. Main results: The results showed that the LS-SVM, which utilized a combination of multi-scale and multi-domain features, achieved better classification performance than the DBN and RF using multi-scale or multi-domain features alone or together, with average sensitivity, specificity, and accuracy of 0.821, 0.955 and 0.820 on the testing set, respectively. Significance: PCG signal analysis provides efficient measurement information regarding CHF severity and is a promising noninvasive method for ACC/AHA HF stage classification.