Under the sharp turn condition, especially on low adhesion coefficient roads, drift motion can improve vehicle agility and ensure safety. During drift motion, the large sideslip angle and rear wheel slip as well as the saturation of lateral tyre force result in the complex nonlinear dynamic behaviour, such as non-unique equilibrium point and unstable vehicle dynamic. Therefore, this paper focuses on the analysis of dynamic characteristics and the design of both the equilibrium point and feedback controller for drift motion. First, a dynamics model, in which the rear wheel slip ratio is treated as a parametric variable and the influence of rear wheel lateral force on the drift motion is explicitly expressed, is established. Then the expression of steady-state yaw rate and the virtual control input is derived, and the error dynamic model is presented furthermore. To design the equilibrium point, in this paper the effect of rear tyre slip angle and slip ratio on the equilibrium point is discussed, and the condition of stable equilibrium point is proposed. In addition, the design of desired rear tyre slip angle by synthesising the cornering performance during drift motion is presented. For the drift controller design, the main idea is to design the stabilisation controller for the nonlinear dynamic system with the stable equilibrium point and to calculate static feedback gain by means of Lyapunov stability theory. To illustrate the characteristics of drift motion, the influence of the vehicle speed and rear wheel slip ratio on the vehicle path and the low damping characteristics of the dynamic system on the control performance are analysed by different simulation conditions. Moreover, the performance and effectiveness of the proposed drift control are verified by simulation.