Cloud computing and edge computing models are popularly applied in emerging applications, such as smart homes, smart parks, and connected autonomous vehicles for large-scale live video analytics. Cloud computing-based models transfer all data to the cloud for video analytics, which burdens network bandwidth and increases the data transmission overhead. Edge computing mode enables video data to be processed at the edge node, thereby reducing the bandwidth overhead. Existing edge computing-based models optimize the performance, but they still have defects in three perspectives: 1) enabling end users to control video content in a real-time format; 2) efficiently locating and transferring the user region of interest (ROI) video data in the video stream; and 3) adapting to various network conditions. To tackle these challenges, we proposed an intelligent elastic edge framework for live video analytics, known as ElasticEdge. ElasticEdge enables the interaction between the end user and the edge node. Elasticity is reflected in two perspectives: 1) the dynamic changes of user requirements and 2) the dynamic changes in network conditions. In addition, ElasticEdge transmits the video stream to the end users based on the tradeoff between the amount of video data and users’ ROI to meet various network conditions. To validate ElasticEdge, we conducted experiments to study its performance in comparison to RTFace. The experimental results show that ElasticEdge has a significant edge over RTFace in terms of data transmission. Using 1/16 reserved images, ElasticEdge saves 75% bandwidth and reduces latency by approximately 10% compared with RTFace. We also find that ElasticEdge adapts to various network conditions when streaming videos, i.e., it can reliably obtain essential information with low latency even when the network condition is poor.