With the rapid development of deep neural networks, the emerging of big data as well as the advancement of computational power, Deep Neural Network (DNN) has been widely applied in various safety-critical domains such as autonomous driving, automatic face recognition, and aircraft collision avoidance systems. Traditional software systems are implemented by developers with carefully designed programming logics and tested with test cases which are designed based on specific coverage criteria. Unlike traditional software development, DNN defines a data-driven programming paradigm, i.e., developers only design the structure of networks and the inner logic is reflected by weights which are learned during training. Traditional software testing methods cannot be applied to DNN directly. Driven by the emerging demand, more and more research works have focused on testing of DNN, including proposing new testing evaluation criteria, generation of test cases, etc. This study provides a thorough survey on testing DNN, which summarizes 92 works from related fields. These works are systematically reviewed from three perspectives, i.e., DNN testing metrics, test input generation, and test oracle. Existing achievements are introduced in terms of image processing, speech processing, and natural language processing. The datasets and tools used in DNN testing are surveyed and finally the thoughts on potential future research directions are summarized on DNN testing, which, hopefully, will provide references for researchers interested in the related directions.