Soft robots have advantages such as low weight and compact size compared to rigid robots. Variable stiffness is one of the key methods of improving the performance of a soft robot. The soft gripper grasps objects of various shapes or sizes based on the variable stiffness. In a previous study, we validated the variable stiffness mechanism where flexible and rigid segments were connected alternately in series. This paper presents a soft variable stiffness gripper that can be used to control the stiffness by pulling tendons. The soft gripper has three variable stiffness structures acting as fingers and the stiffness can be controlled using two motors by winding tendons. To understand the tendency of the stiffness variation and determine the design parameters, a compliant mechanism was developed using a pseudo-rigid-body model (PRBM). The experimental results show that the difference between the lowest and highest stiffness values of the fabricated variable stiffness gripper was 5.6 times the original. Similarly, the difference in the gripping weight was 19 times. Using the experimental results, the variable stiffness gripper can be designed and manufactured based on the required stiffness and used to grip various types of objects.