The unconstrained dynamic deformation of feeding paper at the outlet of the paper path under gravity was studied. Kinematic model was established for the paper passing the paper path outlet. The dynamic deformation of paper was described through nonlinear equations. The dynamic deformation motion of paper was solved by numerical calculation. The effects of different speed and outlet angle on the paper deformation were analyzed. When the feeding speed was increased from 100 mm/s to 500 mm/s, the maximal curvature of paper was reduced from 0.0058 to 0.0029, and the bending deformation of paper decreased with the increasing feeding speed. When the paper outlet angle was increased from 20° to 40° , the paper descending height decreased from 36.1 mm to 28.5 mm. The motion position of the paper edge could be changed by adjusting the paper feeding speed and the outlet angle of the paper path, which provided design reference for the accurate pre-estimated positioning of paper feeding.