The quality of apple picking affects the sales of apples, and the grasping force of the end effector of an apple picking robot is very important for apple picking. It is easy to cause apple damage due to excessive contact force, or when the contact force is too small to grasp the apple. However, the current research lacks an analysis of the minimum stable grasping force of apples. Therefore, in order to realize the stable grasping of apples by the end-effector of a picking robot and reduce fruit damage, this study first analyzes the grasping stability of the end-effector based on the force closure theory, and comprehensively considers the force closure constraints, nonlinear friction cone constraints and the introduction of torque constraints. Next, the constraint conditions are processed using an obstacle function, and a penalty factor is introduced to construct an optimization model of the contact force distribution of the end-effector. Then, the improved Newton method is used to grasp and solve the contact force distribution model. Under the premise of selecting the penalty factor, the optimal contact force of grasping an apple is determined using a method of numerical example simulation analysis, and the validity of the solution is verified. In order to verify the reliability of the contact force distribution optimization model, the practical significance of the method for apple grasping is verified in an actual grasping experiment. The actual experiment shows that the method can provide the minimum stable grasping force to the end-effector to achieve stable grasping.