This paper presents a novel structure-controlled variable stiffness robotic gripper that enables adaptive gripping of soft and rigid objects with a wide range of compliance. With the structure-controllable principle, the stiffness is controlled by the mechanical structure configurations rather than by material properties or electronic means. The principle is realized by changing the effective second moment of area of the gripper finger through rotating a built-in flexure hinge shaft. Based on this principle, the states of the stiffness can be continuously, instead of discretely, studied and assessed over the intermediate states from compliant to almost completely rigid. A variable stiffness mechanism has been developed to demonstrate the validity of the proposed principle. It enables that the finger stiffness and gripping position are independently controlled. With the introduction of flexure hinges, the undesired lateral buckling resulted from the rotation of a normal leaf spring is eliminated. In addition, a two-finger parallel gripper with this variable stiffness mechanism is developed which can provide the grasping stiffness according to the grasping task requirements. The effectiveness of the gripper has been demonstrated to handle the objects range from light, fragile to heavy, rigid without using any feedback loop or soft pads. Note to Practitioners —This work was inspired by the fact that the capability of variable stiffness in the robot actuator can reduce the undesired impacts to the robot arms. It can also allow a safer interaction between robot and human. Gripping of objects with uncertainties in shapes and position, as well as large variations in fragility and weight can also benefit from the concept of the variable stiffness. However, existing designs of variable stiffness grippers either have limited stiffness range or bulky configurations. They compromised the practical applications. This paper introduces a design in that a rotating flexure hinge shaft is embedded inside the robotic gripper finger. The mechanical stiffness of such fingers can be varied by changing the rotation angle of the flexure hinges. We present the working principle supported by mathematical models in the design and development. We also show an example design of a two-finger parallel gripper equipped with the VSFs. Extensive experiments demonstrated that the gripper is effective in gripping objects with wide range of uncertainties. Such gripper design avoids the use of soft pads as well as closed-loop control and high-precision sensors. In the future work, we shall implement such grippers for actual industrial applications.