The demand for flexible grasping of various objects by robotic hands in the industry is rapidly growing. To address this, we propose a novel variable stiffness gripper (VSG). The VSG design is based on a parallel-guided beam structure inserted by a slider from one end, allowing stiffness variation by changing the length of the parallel beams participating in the system. This design enables continuous adjustment between high compliance and high stiffness of the gripper fingers, providing robustness through its mechanical structure. The linear analytical model of the deflection and stiffness of the parallel beam is derived, which is suitable for small and medium deflections. The contribution of each parameter of the parallel beam to the stiffness is analyzed and discussed. Also, a prototype of the VSG is developed, achieving a stiffness ratio of 70.9, which is highly competitive. Moreover, a vision-based force sensing method utilizing ArUco markers is proposed as a replacement for traditional force sensors. By this method, the VSG is capable of closed-loop control during the grasping process, ensuring efficiency and safety under a well-defined grasping strategy framework. Experimental tests are conducted to emphasize the importance and safety of stiffness variation. In addition, it shows the high performance of the VSG in adaptive grasping for asymmetric scenarios and its ability to flexible grasping for objects with various hardness and fragility. These findings provide new insights for future developments in the field of variable stiffness grippers.