LED die bonder is a high precision packaging machine and needs proper tolerance design to ensure its high performance requirements and low manufacturing costs. The related tolerance design methods, such as worst-case method and statistical method, mainly focus on two-dimensional cases in tolerance design. However, tolerance design for LED die bonder needs to deal with three-dimensional cases. To solve the problem, a new method for tolerance design based on Multi-body systems is presented. According to the motion characteristics of the related assembly component parts of LED die bonder, the motion equations in ideal and actual situation for die bonding are given respectively which use the principle of Multi-body systems and the homogeneous transform matrix. By solving the motion equation, we can obtain the tolerances of the related assembly component parts.