Soft grippers, characterized by their compliant and adaptable structures, are increasingly utilized in industries such as food handling and electronics assembly. However, the controllers designed for soft grippers often lack high-precision feedback and real-time dynamic adaptability, limiting their performance in tasks requiring speed, force accuracy, or complex interaction with unpredictable environments. This paper presents a bio-inspired fin-ray gripper with force-position hybrid control, designed to enhance the grasping of delicate and irregularly shaped objects. Inspired by fish fin structures, the gripper utilizes TPU 95A material for its grasping end, featuring a trapezoidal geometry with transverse notches to increase contact area and friction, thereby improving adaptability and stability. An adaptive PID controller, incorporating just-in-time learning (JITL) and real-time sensor feedback, dynamically adjusts force and position parameters to prevent excessive deformation and ensure safety. Experimental validation on a robotic arm demonstrates superior performance in grasping fragile, soft, and rigid objects compared to traditional position control, with reduced object and gripper deformation.