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This paper investigates the output feedback control problem of a vehicle platoon with a constant time headway (CTH) policy, where each vehicle can communicate with its consecutive vehicles. Firstly, based on the integrated-sliding-mode (ISM) technique, a neural adaptive sliding-mode control algorithm is developed to ensure that the vehicle platoon is moving with the CTH policy and full state measurement. Then, to further decrease the measurement complexity and reduce the communication load, an output feedback control protocol is proposed with only position information, in which a higher order sliding-mode observer is designed to estimate the other required information (velocities and accelerations). In order to avoid collisions among the vehicles, the string stability of the whole vehicle platoon is proven through the stability theorem. Finally, numerical simulation results are provided to verify its effectiveness and advantages over the traditional sliding-mode control method in vehicle platoons.