The black-box working mechanism of artificial neutral network brings the confusion of interpretability. Therefore, a rule inference network is proposed based on rule-base inference methodology using the evidential reasoning approach (RIMER). It is interpretable by the rules and the inference engine in RIMER. In the present work, the partial derivatives of inference functions are proved as the theoretical fundamental of the proposed model. The framework and the learning algorithm of rule inference network for classification are presented. The feed forward of rule inference network using the inference process in RIMER contributes for the interpretability. Meanwhile, parameters in belief rule base such as attribute weights, rule weights and belief degree of consequents are trained by gradient descent as in neural network for belief rule base establishment. Moreover, the gradient is simplified by proposing the "pseudo gradient" to reduce the learning complex during the training process. The experimental results indicate the advantages of proposed rule inference network on both interpretability and learning capability. It shows that the rule inference network performs well when the scale of the training dataset is small, and when the training data scale increases, it also achieves comforting results.