This paper selects delta high-speed parallel robot with three degrees of freedom as the research object. The trajectory planning strategies of Cartesian space and angular displacement, angular velocity and angular acceleration of three joints in high-speed handling are studied. Firstly, the critical trajectory points starting point and end point, and points for obstacle avoidance height are set up, and then according to the inverse kinematics model of the robot, a point-to-point “door” type moving trajectory is established, and the mapping relationship between the motion characteristics of the operating space and the motion characteristics of the joint space is established by using the 4-3-4 degree polynomial motion law in the operating space. However, aiming at the higher energy consumption of 4-3-4 degree polynomial interpolation caused by longer the trajectory, and difficult control of obstacle avoidance height, one key point is added. Thereby, the motion rules are interpolated by 4-3-3-4 degree polynomial interpolation, and the mapping relationship between the motion characteristics of the operating space and the motion characteristics of the joint space is established. Two trajectory planning methods are simultaneously simulated under the same keys points and the same trajectory time range. The motion characteristics of the joint rotation angle of the parallel robot between polynomial interpolations are respectively compared. The results show that the trajectory planning method based on 4-3-3-4 degree polynomial interpolation in joint space has obvious advantages in improving the running state of the delta parallel robot and reducing the energy consumption of the system.