Predicting churning customers in advance allows marketers to retain existing and valuable customers, and to develop a customer churn predicting model is a key issue of customer relationship management in modern marketing. In this paper, a product-based Recurrent Neural Network (pRNN) approach is proposed for customer churn prediction in telecommunication sector. In the proposed model, RNN with long short-term memory units is used to learn sequential patterns from customer data changing over time, and the product operation is introduced before recurrent layer to learn high-order interaction between features. pRNN is applied on a real-world telecommunication dataset; experiment results demonstrate that pRNN significantly outperforms other comparison models.