Traffic oscillations, often induced by repetitive acceleration and deceleration maneuvers in vehicles’ car-following behaviors, can cause many negative impacts on the traffic flow. With the development of connected and automated vehicle (CAV) technologies recently, scholars have made numerous effects on mitigating the propagation of traffic oscillations through a variety of advanced CAV control strategies, especially those related to the CAV platoon control. Different from the previous works, this paper proposed a platoon-based adaptive cruise control (PACC) strategy for CAV platoon to mitigate the traffic oscillations. The strategy is designed based on the novel and unique leader-following (LF) information topology. Built on the classical proportional-derivative (PD) controller that is implemented in the adaptive cruise control (ACC) strategy of autonomous vehicles (AVs), the PACC strategy is exquisitely designed to ensure the string stability of entire CAV platoon and the critically damped condition of each following CAV in the platoon. Credit to the rapid response of following CAV to the vibration of leading CAV’s dynamic status under LF information topology and the thorough consideration of string stability and damping characteristics in the PD controller design, the PACC strategy enables the CAV platoon to mitigate the traffic oscillations more efficiently than the existing cooperative adaptive cruise control (CACC) and ACC strategies. The numerical experiment for the mixed traffic flow on a single-lane ring road indicates that, when the CAV platoon adopts the PACC strategy, the performance of traffic flow in terms of operational efficiency, driving safety, passenger’s comfort, and fuel economy is substantially enhanced, compared with CACC and ACC strategies. In addition, the performance of PACC strategy gradually improves with the increase of market penetration rate (MPR) of CAVs and length of CAV platoon. Overall, the proposed PACC strategy is a promising solution to the mitigation of traffic oscillation under the CAV environment.