This study aimed to propose a kind of flexible pneumatic gripper with leaf spring skeleton and made analysis on the griping process with apples. The deformation of the leaf spring can be equivalent to the large deflection deformation of the elastic cantilever beam, and the differential method was used to solve the large deformation equation with help of MATLAB. Static model of the cantilever had been built both under driving load and grasping load. The deformation of the leaf spring and the required pressure were solved using a differential method. The flexible gripper can steadily grasp the objective and it will have a broad prospect in the fruit sorting field because of the strong self-adaptability.