In this paper, a Pythagorean-Hodograph (PH) curve-based pick-and-place operation trajectory planning method for Delta parallel robots is proposed, which realizes the flexible control of pick-and-place operations to meet the requirements of various practical scenarios. First, according to the geometric relationship of pick-and-place operation path, different pick-and-place operations are classified. Then trajectory planning is carried out for different situations, respectively, and in each case, the different polynomial motion laws adopted by the linear motion segment and the curved motion segment are solved. Trajectory optimization is performed with the motion period as optimization objective. The proposed method is easier to implement, and at the same time satisfies the safety, optimization, mobility, and stability of the robot; that is, the proposed method realizes obstacle avoidance, optimal time, flexible control of the robot trajectory, and stable motion. Simulations and experiments verify the effectiveness of the method proposed in this paper. The proposed method can not only realize the fast, accurate, and safe operation in intelligent manufacturing fields such as rapid classification, palletizing, grasping, warehousing, etc., but its research route can also provide a reference for trajectory planning of intelligent vehicles in logistics system.