Visual Commonsense Reasoning (VCR) predicts an answer with corresponding rationale, given a question-image input. VCR is a recently introduced visual scene understanding task with a wide range of applications, including visual question answering, automated vehicle systems, and clinical decision support. Previous approaches to solving the VCR task generally rely on pre-training or exploiting memory with long dependency relationship encoded models. However, these approaches suffer from a lack of generalizability and prior knowledge. In this paper we propose a dynamic working memory based cognitive VCR network, which stores accumulated commonsense between sentences to provide prior knowledge for inference. Extensive experiments show that the proposed model yields significant improvements over existing methods on the benchmark VCR dataset. Moreover, the proposed model provides intuitive interpretation into visual commonsense reasoning. A Python implementation of our mechanism is publicly available at https://github.com/tanjatang/DMVCR