This research presents a soft gripper for apple harvesting to provide constant-pressure clamping and avoid fruit damage during slippage, to reduce the potential danger of damage to the apple pericarp during robotic harvesting. First, a three-finger gripper based on the Fin Ray structure is developed, and the influence of varied structure parameters during gripping is discussed accordingly. Second, we develop a mechanical model of the suggested servo-driven soft gripper based on the mappings of gripping force, pulling force, and servo torque. Third, a real-time control strategy for the servo is proposed, to monitor the relative position relationship between the gripper and the fruit by an ultrasonic sensor to avoid damage from the slip between the fruit and fingers. The experimental results show that the proposed soft gripper can non-destructively grasp and separate apples. In outdoor orchard experiments, the damage rate for the grasping experiments of the gripper with the force feedback system turned on was 0%; while the force feedback system was turned off, the damage rate was 20%, averaged for slight and severe damage. The three cases of rigid fingers and soft fingers with or without slip detection under the gripper structure of this study were tested by picking 25 apple samples for each set of experiments. The picking success rate for the rigid fingers was 100% but with a damage rate of 16%; the picking success rate for soft fingers with slip detection was 80%, with no fruit skin damage; in contrast, the picking success rate for soft fingers with slip detection off increased to 96%, and the damage rate was up to 8%. The experimental results demonstrated the effectiveness of the proposed control method.