Stance detection is an important task, which aims to classify the attitude of an opinionated text toward a given target. In this paper, we develop an interpretable neural production system for stance detection (NPS4SD). NPS4SD is an end-to-end deep learning model, which consists of a set of knowledge rules that are applied by binding with specific entities. NPS4SD consists of two main components: a pretrained model for learning the text representation and a variable binding network (VBN) to bind the knowledge rules with text entities. Extensive experiments are conducted to evaluate the effectiveness of the proposed NPS4SD model on three real-world datasets with in-domain, cross-target and zero-shot setups. Experimental results demonstrate that NPS4SD achieves substantially better performance than the strong competitors for the stance detection task.