Parallel mechanisms could be hardly used in contour tracking because of their mechanism features. This study proposed a link-space real time contour tracking for a 3 DOF (Z、α and β) hydraulic parallel mechanism. The essence of this approach is to convert control points of command trajectory to link space by inverse kinematics. A real-time interpolator was created and the multi-axis cross-coupled pre-compensation control (MCCPM) was constructed for link-space contour tracking. It was shown that a contour-accurate trajectory tracking could be performed which was impossible in the original Z-α-β space. Other advantages of this link-space approach were time efficiency and the uniform tracking velocity.