Objective: Here in this study, we focus on solving the pick-and-place problem of the food packaging boxes in different positions. Methods: A novel design of under-actuated robotic hand was proposed, and two motion patterns of the robotic hand were realized based on cable-pulley transmission, which were parallel gripping and adaptive gripping between the fingers. On this basis, the statics of the robotic hand was analyzed through the principle of virtual work, and the gripping forces between the fingers were obtained. Results: The force between the fingers can ensure the effective gripping of the packaging box no matter whether the box is in the middle position or not. Conclusion: The performance of the parallel gripping motion is stable, and the adaptive gripping between the fingers can be realized.