This paper proposes a three-axis coupling controller designed to improve the contouring accuracy in machining of 3D nonlinear contours. The proposed coupling controller is based on an innovative 3D contour error model and a PID control law. The novel contour error model provides almost exact calculation of contour errors in real-time for arbitrary contours and can be integrated with any type of existing interpolator. In the proposed method, three axes of motion are coordinated by the proposed coupling controller along with a proportional controller for each axis. The proposed contour error model and coupling controller are evaluated through computer simulations. The simulation results show that the proposed 3-axis coupling controller with the new contour error model substantially can improve the contouring accuracy by order of magnitude compared with the existing uncoupled controllers in high-speed machining of nonlinear contours.