Deep neural networks achieve high predictive accuracy by learning latent representations of complex data. However, the reasoning behind their decisions is difficult for humans to understand. On the other hand, rule-based approaches are able to justify the decisions by showing the decision rules leading to them, but they have relatively low accuracy. To improve the interpretability of neural networks, several techniques provide post-hoc explanations of decisions made by neural networks, but they cannot guarantee that the decisions are always explained in a simple form like decision rules because their explanations are generated after the decisions are made by neural networks.In this paper, to balance the accuracy of neural networks and the interpretability of decision rules, we propose a hybrid technique called rule-constrained networks, namely, neural networks that make decisions by selecting decision rules from a given ruleset. Because the networks are forced to make decisions based on decision rules, it is guaranteed that every decision is supported by a decision rule. Furthermore, we propose a technique to jointly optimize the neural network and the ruleset from which the network select rules. The log likelihood of correct classifications is maximized under a model with hyper parameters about the ruleset size and the prior probabilities of rules being selected. This feature makes it possible to limit the ruleset size or prioritize human-made rules over automatically acquired rules for promoting the interpretability of the output. Experiments on datasets of time-series and sentiment classification showed rule-constrained networks achieved accuracy as high as that achieved by original neural networks and significantly higher than that achieved by existing rule-based models, while presenting decision rules supporting the decisions.