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The internal stability and string stability of vehicle platoon system with communication delay are studied. Firstly, the high-dimensional vehicle platoon closed-loop control system is divided into several equivalent low-dimensional subsystems by matrix similarity transformation, which greatly reduces the analytical difficulty and computational complexity of internal stability analysis. On this basis, the direct method is used to solve the critical virtual root of vehicle platoon subsystems, the accurate delay boundary is deduced accordingly, and the sufficient and necessary conditions for the internal stability of the system are obtained. Then, in order to ensure the disturbance is not amplified in the process of propagation along the vehicle platoon, The string stability conditions of the vehicle platoon system are given by analyzing the error transfer function along the vehicles, and the guiding principles of delay and controller parameters are given. Finally, the effectiveness of the proposed stability analysis method is verified by simulation.