Time series clustering is usually an essential unsupervised task in cases when category information is not available and has a wide range of applications. However, existing time series clustering methods usually either ignore temporal dynamics of time series or isolate the feature extraction from clustering tasks without considering the interaction between them. In this article, a time series clustering framework named self-supervised time series clustering network (STCN) is proposed to optimize the feature extraction and clustering simultaneously. In the feature extraction module, a recurrent neural network (RNN) conducts a one-step time series prediction that acts as the reconstruction of the input data, capturing the temporal dynamics and maintaining the local structures of the time series. The parameters of the output layer of the RNN are regarded as model-based dynamic features and then fed into a self-supervised clustering module to obtain the predicted labels. To bridge the gap between these two modules, we employ spectral analysis to constrain the similar features to have the same pseudoclass labels and align the predicted labels with pseudolabels as well. STCN is trained by iteratively updating the model parameters and the pseudoclass labels. Experiments conducted on extensive time series data sets show that STCN has state-of-the-art performance, and the visualization analysis also demonstrates the effectiveness of the proposed model.