The healthcare industry has made significant progress in the diagnosis of heart conditions due to the use of intelligent detection systems such as electrocardiograms, cardiac ultrasounds, and abnormal sound diagnostics that use artificial intelligence (AI) technology, such as convolutional neural networks (CNNs). Over the past few decades, methods for automated segmentation and classification of heart sounds have been widely studied. In many cases, both experimental and clinical data require electrocardiography (ECG)-labeled phonocardiograms (PCGs) or several feature extraction techniques from the mel-scale frequency cepstral coefficient (MFCC) spectrum of heart sounds to achieve better identification results with AI methods. Without good feature extraction techniques, the CNN may face challenges in classifying the MFCC spectrum of heart sounds. To overcome these limitations, we propose a capsule neural network (CapsNet), which can utilize iterative dynamic routing methods to obtain good combinations for layers in the translational equivariance of MFCC spectrum features, thereby improving the prediction accuracy of heart murmur classification. The 2016 PhysioNet heart sound database was used for training and validating the prediction performance of CapsNet and other CNNs. Then, we collected our own dataset of clinical auscultation scenarios for fine-tuning hyperparameters and testing results. CapsNet demonstrated its feasibility by achieving validation accuracies of 90.29% and 91.67% on the test dataset.