Congestive heart failure (CHF) is a serious pathophysiological condition with high morbidity and mortality, which is hard to predict and diagnose in early age. Artificial intelligence and deep learning combining with cardiac rhythms and physiological time series provide a potential to help with solving it. In this study, we proposed a novel method that combines convolutional neural network (CNN) and distance distribution matrix (DDM) in entropy calculation to classify CHF patients from normal subjects, and demonstrated the effectiveness of this combination. Specifically, three entropy methods were used to generate the distribution matrixes from a 300-point RR interval (i.e., the time interval between the successive cardiac cycles) time series, which are Sample entropy (SampEn), fuzzy local measure entropy (FuzzyLMEn) and fuzzy global measure entropy (FuzzyGMEn). Then, three high representative CNN models, i.e. AlexNet, DenseNet and SE_Inception_v4 were chosen to learn the pattern of the data distributions hidden in the generated distribution matrixes. All data used in our experiments were gathered from the MIT-BIH RR Interval Databases (http://www.physionet.org). A total of 29 CHF patients and 54 normal sinus rhythm (NSR) subjects were included in this study. The results showed that the combination of FuzzyGMEn-generated DDM and Inception_v4 model yielded the highest accuracy of 81.85% out of all proposed combinations.