In this paper, we present a novel compliant robotic gripper with three variable stiffness fingers. While the shape morphing of the fingers is cable-driven, the stiffness variation is enabled by layer jamming. The inherent flexibility makes compliant gripper suitable for tasks such as grasping soft and irregular objects. However, their relatively low load capacity due to low structural stiffness limits their applications. Variable stiffness robotic grippers have the potential to address this challenge as their stiffness can be tuned on demand based on the needs of tasks. In our design, the compliant backbone of finger is made of 3D printed PLA materials sandwiched with thin film materials. The working process of the robotic gripper follows two basic steps. First, the compliant skeleton is bent to a desired shape by actuating a tension cable via a servo motor. Second, upon application of a negative pressure by a vacuum pump, the finger is stiffened up owing to the increasing of the friction between contact surfaces of layers which prevents their relative movement. As a result, their load capacity will be increased proportionally. Test for stiffness of individual finger and load capacity of the robotic gripper are conducted to validate capability of the design. The results showed a 180-fold increase in stiffness of individual finger and a 30-fold increase in gripper's load capacity.