A robot hand is required to generate a large grasping force. Furthermore, it is required that one finger should possess multiple degrees of freedom and the fingertips should be positioned freely to grasp and manipulate objects of various sizes and shapes. A function to adjust the stiffness is also required to control the force and realize stable grasping. The development of a hand with these functions at a high level is a technical problem. We propose a multi-degree-of-freedom finger module that uses pneumatic cylinders and a parallel link mechanism. The proposed hand has adjustable stiffness while maintaining high grasping force-to-weight ratio. In addition, the proposed hand was able to estimate the external force acting on the fingertip from the differential pressure and a kinematics model. By using the estimated external force for control, adjustable stiffness was realized without using a force sensor. This paper also describes the design method of the finger module. We experimentally confirmed that the proposed hand was able to satisfy various target specifications. In addition, it was able to realize multiple functions of a hand using a compact mechanism.