This paper describes the design and development of a novel dual manipulator system for table tennis as an application of Human-Robot Interaction (HRI). To hit table tennis quickly, a method to obtain time-constrained trajectory joining two way-points is developed and implemented. Because the quintic polynomial trajectory is a smooth curve and can reduce jerk, it appears to be excellent choice for hitting task. Five phase quintic polynomials are adopted to fit the smooth trajectory in joint space under the constraint of robotic kinematics parameters. The boundary conditions of five phase qunitic polynomials used to compute the trajectories are discussed under different initial kinematics conditions. Experimental results of actual robotic system with dual manipulators and vision system show that the proposed method works well.