In vehicle platoon control, traditional control strategies struggle to simultaneously meet the requirements of system robustness and high-precision tracking, especially when facing external disturbances and model uncertainties, which exacerbates the issue. This paper proposes a fusion algorithm (LFC-MSE) that combines linear feedback control with vehicle motion state estimation to enhance the accuracy of the following vehicle′s speed and angular velocity, thereby mitigating the adverse effects of external disturbances and communication delays. By utilizing feedback linearization, the nonlinear system of vehicle platooning is transformed into a linear system for solution, and a controller for the vehicle platoon system is designed. In terms of communication delay, the motion state of the vehicle is estimated to improve the response speed and control accuracy of the entire system. Finally, in the CarSim-Simulink co-simulation environment, the dynamic model, parameter model, and control model of the vehicle platoon are established to simulate and validate the proposed LFC-MSE algorithm. The simulation results show that under the control of this algorithm, the lateral error of the following vehicle relative to the leading vehicle is within 0.5 m, and the longitudinal trajectory error is within 1.5 m. Moreover, the LFC-MSE control scheme performs better in maintaining platoon stability, response speed, and reducing energy consumption.