In this paper, the problem of steady drift control of vehicles is studied, and an autonomous vehicle drifting control method based on improved guaranteed cost control is proposed. Firstly, a three-degree-of-freedom vehicle dynamics model is constructed, in which the influence of tire nonlinearity is considered. Then the equilibrium point of the vehicle system is calculated by using the established model, and the relationship between the stable equilibrium point, the unstable equilibrium point and the vehicle drift state is analyzed based on the phase plane method. Then, the Koopman operator theory is introduced to derive an approximate linear model that retains the nonlinear characteristics of the vehicle system. At the same time, the existence conditions and construction methods of the improved guaranteed cost control law that can deal with system constraints are given. A state feedback controller based on the improved guaranteed cost is designed according to the approximate linear model, which can maintain the vehicle’s state around the desired unstable equilibrium point while ensuring control constraints. Finally, experiments on the Carsim-Simulink simulation platform show that the proposed method is effective in achieving autonomous vehicle drifting and ensuring vehicle safety.