During the picking process of the apple harvesting robot, the attitude of the end effector holding the apple and the movement method of separating the apple directly affect the success rate of picking. In order to improve the stability of the picking process, reduce the gripping force, and avoid apple dislodgement and damage, this work studies the new apple-picking pattern of the flexible three-fingered end-effector based on the analysis of the existing apple-picking pattern. First, two new three-finger grasping postures for wrapping the apple horizontally and vertically on the inside of the fingers are proposed, and a new method of separating the stem with a circular-pull-down motion of the end-effector picking the apple is designed. Then, the pressure on the apple under different picking patterns was analyzed, and a branch–stem–apple simulation model was established. Combining the constraint conditions such as the angle between the apple stem and the vertical direction, the movement speed, the root impulse, and so on, the optimal angle of apple circular movement and the force required to realize the movement are obtained through dynamic simulation experiments. Finally, the experiments of apple picking patterns were carried out with the flexible three-fingered end-effector. The experiment shows that the best angle for apple picking is 15°~20° using the circular-pull-down movement separation method. In terms of average grasping force peaks and pressures, the combination of the vertical holding posture of the inner finger and the circular-pull-down movement separation method is the best picking pattern. In this pattern, the average peak exerts force on the inner side of a single finger is about 8.52 N, and the pressure is about 20.9 KPa.