We propose a new CogQA framework for multi-hop reading comprehension question answering in web-scale documents. Founded on the dual process theory in cognitive science, the framework gradually builds a cognitive graph in an iterative process by coordinating an implicit extraction module (System 1) and an explicit reasoning module (System 2). While giving accurate answers, our framework further provides explainable reasoning paths. Specifically, our implementation based on BERT and graph neural network efficiently handles millions of documents for multi-hop reasoning questions in the HotpotQA fullwiki dataset, achieving a winning joint F₁ score of 34.9 on the leaderboard, compared to 23.1 of the best competitor.