：Taking 3-DOF Delta parallel manipulator as the research object, different trajectory planning methods in operating and joint space under high-speed operations are researched. Combined with practical requirements, the motion trajectory of point to point is defined through a set of critical path points. In the operating space, based on the inverse kinematics model, the mapping relation of motion characteristics from operating space to joint space is established according to the 3-4-5 polynomial motion law. In the joint space, based on the forward kinematics model, the mapping relation of motion characteristics from joint space to operating space is established according to the quintic non-uniform rational B-spline (NURBS) motion law. Under same critical path points and time, simulations and analyses of movement characteristics (the position, velocity and acceleration of joint) on the two trajectory planning methods are proposed, and the comparison experiment is carried out. The results show that the trajectory planning method of quintic NURBS motion law in joint space has an obvious superiority in reduction of the vibration of the manipulator in movement and the motor power consumption.