To establish a rigid dynamics model of a 3 degree-of-freedom decoupled parallel mechanism（a 3-CP,a,RR decoupled parallel mechanism） and sliding mode controller,the structure component of the mechanism is described and the kinematics is revealed by analyzing the kinematics constraints. The analysis of kinematics constraint shows that the translational displacement of the mechanism is completely decoupled in the three orthogonal directions,and the rotation joints of the limb distal link are the negative kinematics pairs.According to the result of analysis,the dynamics model of the 3-CP,a,RR decoupled parallel mechanism is established by using the Lagrange equation. Meanwhile,a controller is designed by means of the sliding mode surface,and the system stability is analyzed via Lyapunov function. Finally,the linear velocity and driving force are analyzed through a numerical example. The validity of theoretical analysis and numerical example are demonstrated by the virtual simulation results in ADAMS. At the same time,the validity and stability of the sliding mode controller are also demonstrated. The research provides a theoretic foundation for research on the prototype manufacturing and real-time control system.