Due to the increasing demand for autonomous driving, cyber-attacks detection nowadays receives significant attention. Among several different types of attacks, Denial-of-Service (DoS) attacks can consume resources and cause the system under attack to stop responding, which can be considered a time delay model affecting the response of the attacked system. To detect the possible DoS attacks in Cooperative Adaptive Cruise Control platoon model, an adaptive observer design is proposed in this paper, where the time delay caused by DoS attacks can be fast and accurately estimated. To highlight the performance of the proposed adaptive observer, numerical simulations are applied and the performance is compared against the sliding mode observer in terms of the DoS attack time delay estimation convergence and accuracy.