In this paper, we propose a Distributed Intelligent Video Surveillance (DIVS) system using Deep Learning (DL) algorithms and deploy it in an edge computing environment. We establish a multi-layer edge computing architecture and a distributed DL training model for the DIVS system. The DIVS system can migrate computing workloads from the network center to network edges to reduce huge network communication overhead and provide low-latency and accurate video analysis solutions. We implement the proposed DIVS system and address the problems of parallel training, model synchronization, and workload balancing. Task-level parallel and model-level parallel training methods are proposed to further accelerate the video analysis process. In addition, we propose a model parameter updating method to achieve model synchronization of the global DL model in a distributed EC environment. Moreover, a dynamic data migration approach is proposed to address the imbalance of workload and computational power of edge nodes. Experimental results showed that the EC architecture can provide elastic and scalable computing power, and the proposed DIVS system can efficiently handle video surveillance and analysis tasks.