Grasping unstructured objects and sensing the contact force are two vital issues for grippers. However, it is still difficult for most existing grippers to realize these two functions simultaneously. In this article, we revise the traditional fin-ray finger by inserting a series of rigid nodes into the compliant structure and develop an adaptive two-finger gripper. This design linearizes the gripper's deformation-force relationship and enables an intrinsic force sensing ability without any tactile sensor. Experimental results show that the finger has high accuracy in sensing the external force applied at its middle part (average error less than 3%) but much larger errors appear near its two ends. Further experiments indicate that the gripper functions well in sensing the total grasping force (average error less than 8%). Although larger errors are observed in estimating the force distribution at each node, the variation tendency of the sensed force coincides well with the ground truth. Experiments are also carried out on grasping free-form objects and performing pick-and-place operations to further prove the gripper's adaptive grasping and intrinsic force sensing abilities.