Cable-suspended parallel robot is a special type of parallel robot that belongs to the category of flexible robots. End-effector is driven by cables instead of rigid rods to achieve the change of its pose. A three-degree-of-freedom (3-DOF) under-constrained cable-suspended parallel robot is studied in this paper. The inverse kinematics equation of the robot is established based on the vector closed-loop principle. The dynamics equation of the robot is established according to the Lagrange formula. Given the motion trajectory of the robot’s end-effector, and the quintic polynomial is adopted to plan the motion trajectory of the robot. The unplanned and planned position, velocity and acceleration curves in the X, Y and Z directions are obtained. At the points where the velocity changes abruptly, the planned velocity and acceleration curves achieve smooth transition to avoid vibration and impact during the robot’s movement, so as to smooth the motion trajectory of the end-effector. The experimental curves of the length and tension of three cables are basically consistent with the planned expected curves, and the camera tracking trajectory is basically consistent with the motion trajectory after the quintic polynomial planning. Numerical simulation and experimental results validate the correctness of the inverse kinematics and dynamics analysis of the 3-DOF under-constrained cable-suspended parallel robot, as well as the effectiveness of the quintic polynomial planning.