By analyzing structural characteristics of nonlinear vector field for a class of chaotic systems, a new approach to controlling chaos globally and rapidly is put forward. Based on linear state feedback, an independent stable equation of some state variables is separated. Controlled chaotic systems degenerate gradually into stable linear systems. Nonlinear quivering phenomenon is eliminated completely further. The approach can be used to control Lorenz system families or new chaotic systems with similar structures. A class of simple controllers is designed to guarantee that closed-loop systems are globally asymptotically stable at the origin. Numerical examples illustrate the shortcut and the validity of the presented approach in this paper.