Soft robotics has recently gained a significant momentum as a newly emerging field in robotics that focuses on biomimicry, compliancy and conformability with safety in near-human environments. Beside conventional fabrication methods, additive manufacturing is a primary technique to employ to fabricate soft robotic devices. We developed a monolithic soft gripper, with variable stiffness fingers, that was fabricated as a one-piece device. Negative pressure was used for the actuation of the gripper while positive pressure was used to vary the stiffness of the fingers of the gripper. Finger bending and gripping capabilities of the monolithic soft gripper were experimentally tested. Finite element simulation and experimental results demonstrate that the proposed monolithic soft gripper is fully compliant, low cost and requires an actuation pressure below -100 kPa.