Vehicular platoon control can effectively achieve group consensus, improve vehicular running safety and increase road capacity. However, some constraints exist in practical situations due to the limitations of traffic environment in time-varying metrics (time-delay, packet-dropout or interruption) in wireless communication systems. In this work, a distributed model predictive control (MPC) algorithm is proposed for connected vehicle platoon with a focus on switching communication topologies and control strategy under abnormal communications. Firstly, the predecessor-leader following is selected as the basic communication topology, by which the switching communication topology and the desired vehicle spacing policy are established. Secondly, the platoon control algorithm of connected vehicles is established and a set of constraints is analyzed. Thirdly, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}_{2} $ </tex-math></inline-formula> -norm string stability criterion and the asymptotic stability criterion are considered within the proposed MPC. Finally, a co-simulation platform for connected vehicle platoon is developed based on Prescan/Matlab/V2X communication simulator. In addition, the platoon control algorithm is tested in three traffic scenarios including normal communication, leading vehicle with abnormal communication and following vehicle with abnormal communication. The experiments demonstrate that the communication topologies in different communication environments can be switched well in real time through the proposed platoon control algorithm. In addition, the string stability, the consistency of vehicle spacing, speed and acceleration are proven to be guaranteed simultaneously.