This paper introduces a novel gripper that achieves both shape-adaptive grasping and variable stiffness. It is realized through an integration of the “soft gripper,” capable of grasping objects while conforming to their shapes, and a toggle-linkage-based variable stiffness mechanism that does not hinder its grasping ability. Such features enable the gripper to securely manipulate and transport objects where soft/flexible grippers struggled, without being dependent on the shape of the object. Consequently, the proposed mechanism is expected to be capable of firmly grasping objects of various shapes. This paper details the idea, theory, prototype, and experimental validation of the proposed gripper. The paper particularly focuses on, it focuses on the compatibility of shape-adaptive grasping and variable stiffness for the prototype based on the idea, demonstrating its feasibility.