This paper proposes a new variable stiffness soft gripper that enables high-performance grasping tasks in industrial applications. The design of the proposed monolithic soft gripper includes a middle bellow and two side bellows (i.e., fingers). The positions of the fingers are regulated by adjusting the negative pressure in the middle bellow actuator via an on-off controller. The stiffness of the soft gripper is modulated by controlling the positive pressure in the fingers through the use of a proportional air-pressure regulator. It is experimentally shown that the proposed soft gripper can modulate its stiffness by 125% within 250ms. It is also shown that the variable stiffness soft gripper can help improve the safety and performance of grasping tasks in industrial applications.