Cooperative adaptive cruise control (CACC) uses wireless communication between adjacent vehicles to achieve a short inter-vehicle distance (IVD) in automated driving, which improves road throughput. However, the network-induced time delay can violate the stability of vehicle platoons. A conventional time-delay compensation method for a leader-follower type CACC system with front IVD measurement cannot be directly applied to the system with rear IVD measurement because of its specific compensation architecture. This paper proposes a timedelay compensation method using the Smith predictor for the system with rear IVD measurement that can eliminate communication traffic for IVD measurement. Simulations confirm that the proposed method achieves stable CACC as well as the conventional method, while reducing communication traffic.