This article deals with the problem of secure distributed adaptive platooning control of automated vehicles over vehicular ad-hoc networks (VANETs) in the presence of intermittent denial-of-service (DoS) attacks. The platoon, which is wirelessly connected via directed vehicle-to-vehicle (V2V) communication, is composed of a group of following vehicles subject to unknown heterogeneous nonlinearities and external disturbance inputs, and a leading vehicle subject to unknown nonlinearity and external disturbance as well as an unknown control input. Under such a platoon setting, this article aims to accomplish secure distributed platoon formation tracking with the desired longitudinal spacing and the same velocities and accelerations guided by the leader regardless of the simultaneous presence of nonlinearities, uncertainties, and DoS attacks. First, a new logical data packet processor is developed on each vehicle to identify the intermittent DoS attacks via verifying the time-stamps of the received data packets. Then, a scalable distributed neural-network-based adaptive control design approach is proposed to achieve secure platooning control. It is proved that under the established design procedure, the vehicle state estimation errors and platoon tracking errors can be regulated to reside in small neighborhoods around zero. Finally, comparative simulation studies are provided to substantiate the effectiveness and merits of the proposed control design approach on maintaining the desired platooning performance and attack tolerance.