The work aims to design a grasping and packaging robot with 2-RPS-UPU parallel mechanism as the main body and verify whether it has good kinematic performance, in view of the current situation that the grasping and packaging process of bagged food is simple and repetitive, the cost of manual operation is excessively high, and it is likely to cause less and wrong loading. The number and types of degrees of freedom of the mechanism were analyzed with the screw theory and the modified Grubler-Kutzbach formula. Then, the inverse position solution to the kinematics of the mechanism was derived based on "closed-loop analytical method" and "Euler angle representation method", while the forward position solution of the mechanism was analyzed by means of particle swarm optimization algorithm (PSO). Finally, Solidworks software was used to solve the workspace of the mechanism through the "combination of driving dynamics and statics". The proposed robot had three degrees of freedom (two rotations and one movement) and clear position and attitude relationship between the driving joint and the end actuator. It could perform good linear motions. The workspace was like a spider network, featured by a wide range, regular and symmetrical shape and compact structure. The new three-degree-of-freedom parallel robot can meet the motion and working range required by grasping and packaging of bagged food, and it has stable motion and strong reliability.