The work aims to propose a packaging machine based on 3-PRC parallel mechanism (PM) and introduce 3D printing technology in view of the problems caused by the low efficiency and accuracy of the existing lithium battery packaging machine during the packaging process, such as easy clogging and blockage of lithium battery as well as poor sealing performance of package. Firstly, a 3D mathematical model of the 3-PRC PM was established to solve the kinematics equations. Secondly, Matlab simulation method and the travel constraints of the mechanism were adopted to obtain the projected view of the mechanism’s position workspace through the control variable method. Then, cascade PID method was employed to set up the dynamics and control model of the packaging machine to simulate and verify the control algorithm. Finally, based on the simulation model of the packaging machine, physical verification was performed further. The position workspace of the 3-PRC PM had a symmetrical and regular shape, and the cross-section was evenly distributed. During the fixed-point packing process of the packaging machine, the Euler angle changes in all directions were controlled within ±3°, and the actual deviation of the movement in each direction was within ±1 mm, and the circular motion was completed autonomously. The 3-PRC PM can meet the requirements of the position workspace of the lithium battery packaging machine. Simulation and physical verification results prove the rationality and effectiveness of the motion control of the packaging machine, effectively solve the problem of poor motion accuracy during packaging, and can achieve the fast and accurate operation of the battery packaging machine, laying a theoretical foundation for the mechanism’s further optimization design and deep application of 3D printing technology in lithium battery packaging machine.