In recent times, the soft robotics field has been attracting significant research focus owing to its high level of manipulation capabilities unlike traditional rigid robots, which gives room for increasing use in other areas. However, compared to traditional rigid gripper robots, being capable of controlling/obtaining overall body stiffness when required is yet to be further explored since soft gripper robots have inherently less-rigid properties. Unlike previous designs with very complex variable-stiffness systems, this paper demonstrates a soft gripper design with minimum system complexity while being capable of varying the stiffness of a continuum soft robotic actuator and proves to have potential applications in gripping objects of various shapes, weights, and sizes. The soft gripper actuator comprises two separate mechanisms: the pneumatic mechanism for bending control and the mechanical structure for stiffness variation by pulling tendons using stepper motors which compresses the actuator, thereby changing the overall stiffness. The pneumatic mechanism was first fabricated and then embedded into another silicon layer during which it was also merged with the mechanical structure for stiffness control. By first pneumatically actuating the actuator which causes bending and then pulling the tendons, we found out that the actuator stiffness value can be increased up to 145% its initial value, and the gripper can grasp and lift a weight of up to 2.075 kg.