The work aims to propose a grasping robot mechanism with 3PUPaR parallel mechanism as the main structure based on the synthesis method of parallel mechanism structure by the position and orientation characteristics equation (POC) equation aiming at the problems of high labor cost and wrong loading in the process of grasping and assembling food packaging. The degree of freedom, the position and orientation characteristics set, the coupling degree of 3PUPaR parallel mechanism and other topological properties were calculated to verify whether the mechanism had the motion characteristics of space pure movement and establish the inverse kinematics equation of the mechanism. Based on this, the numerical method was used to obtain the mechanism workspace and dexterity and study the influence of different parameters on workspace volume and dexterity. Taking the global dexterity and workspace as the optimization objective, NSGA-II algorithm with Pareto solution was selected to complete the multi-objective optimization. The results showed that the mechanism had a large and continuous workspace.The New 3-DOF parallel robot can meet the motion range of food packaging during grasping and assembly.