Aiming at the requirement of wheel slip tracking control for automatic driving electric vehicle , this paper presents a full-state feedback wheel slip tracking controller based on fast terminal sliding mode state observer. Firstly, a wheel slip rate tracking control model taking the derivative of wheel braking moment as an input is established to avoid the effect of the discontinuity term in the input on the system stability and performance. Secondly, a fast terminal sliding mode state observer with the characteristic of finite time convergence is designed based on finite time stability and fast terminal sliding mode control theory in order to observe the unknown state information of the system in real time. Based on the estimation of the unknown state information of the system, a fast terminal sliding mode tracking control law is designed independently to realize the continuous and fast tracking control of wheel slip. Finally, a model-in-the-loop test system is built using vehicle dynamics simulation software to verify the feasibility and validity of the proposed wheel slip tracking controller.