Cooperative adaptive cruise control (CACC) for human and autonomous self-driving aims to achieve active safe driving that avoids vehicle accidents or traffic jam by exchanging the road traffic information (e.g., traffic flow, traffic density, velocity variation, etc.) among neighbor vehicles. However, in CACC, the butterfly effect is encountered while exhibiting asynchronous brakes that easily lead to backward shock-waves and are difficult to remove. Several critical issues should be addressed in CACC, including (i) difficulties with adaptive steering of the inter-vehicle distances among neighbor vehicles and the vehicle speed, (ii) the butterfly effect, (iii) unstable vehicle traffic flow, etc. To address the above issues in CACC, this paper proposes the mobile edge computing-based vehicular cloud of the cooperative adaptive driving (CAD) approach to avoid shock-waves efficiently in platoon driving. Numerical results demonstrate that the CAD approach outperforms the compared techniques in the number of shock-waves, average vehicle velocity, average travel time and time to collision (TTC). Additionally, the adaptive platoon length is determined according to the traffic information gathered from the global and local clouds.