Objective To meet the requirements of grabbing and sorting of trapezoidal packaging boxes (such as chocolate, biscuit) in production. Methods This paper proposed a single-rope traction drive hinge flexible manipulator for grabbing trapezoidal gift boxes with different gradients and idths, and then introduced the driving principle of the robot mechanical fingers and optimized the related parameters. Results The calculation results showed that the pressure difference between grabbing the maximum and minimum packing box was 1.0311 N. Through global optimization, the torsional spring stiffness coefficient, the preloaded angle and the manipulator joints size were obtained. The curves of joint angular displacement and fingertips opening with the changing pressure were also attained. Conclusion The structure showed very good soft performance, and could achieve adaptive grasping.