Connected cars generate a huge amount of Internet of Things (IoT) sensor information called Controller Area Network (CAN) data. Recently, there is growing interest in collecting CAN data from connected cars in a cloud system to enable life-critical use cases such as safe driving support. Although each CAN data packet is very small, a connected car generates thousands of CAN data packets per second. Therefore, real-time CAN data collection from connected cars in a cloud system is one of the most challenging problems in the current IoT. In this paper, we propose an Edge computing-enhanced network Redundancy Elimination service (EdgeRE) for CAN data collection. In developing EdgeRE, we designed a CAN data compression architecture that combines in-vehicle computers, edge datacenters and a public cloud system. EdgeRE includes the idea of hierarchical data compression and dynamic data buffering at edge datacenters for real-time CAN data collection. Across a wide range of field tests with connected cars and an edge computing testbed, we show that the EdgeRE reduces bandwidth usage by 88% and the number of packets by 99%.