In modern clinical medicine, electrocardiogram (ECG) is a common diagnosis technique of cardiovascular diseases. The purpose of this paper is to propose a novel model-based clustering approach for analyzing ECG data. Our approach is composed of two modules: representation learning and ECG data clustering. In the module of representation learning, a deep generative model referred to as the hyperspherical variational recurrent autoencoder (HVRAE) is developed to extract the representation of observed ECG data, based on the variational autoencoder (VAE) with long short-term memory (LSTM) networks. In the module of ECG data clustering, we develop a nonparametric hidden Markov model (NHMM) based on Dirichlet process in which the number of hidden states is inferred automatically during the learning process. Moreover, the emission density of each hidden state of our NHMM follows a mixture of von Mises-Fisher (VMF) distributions which have better capability for modeling ECG representations than other commonly used distributions (such as the Gaussian distribution). To learn the proposed VMF-based NHMM, we theoretically develop an effective learning algorithm based on variational Bayes. The merits of our model-based clustering approach for analyzing ECG data are verified through experiments on publicly available ECG data sets.