In this paper, a novel robotic gripper design with variable stiffness is proposed and fabricated using a modified additive manufacturing (hereafter called 3D printing) process. The gripper is composed of two identical robotic fingers and each finger has three rotational degrees-of-freedom as inspired by human fingers. The finger design is composed of two materials: acrylonitrile butadiene styrene (ABS) for the bone segments and shape-memory polymer (SMP) for the finger joints. When the SMP joints are exposed to thermal energy and heated to above their glass transition temperature (Tg), the finger joints exhibit very small stiffness, thus allow easy bending by an external force. When there is no bending force, the finger will restore to its original shape thanks to SMP's shape recovering stress. The finger design is actuated by a pneumatics soft actuator. Fabrication of the proposed robotic finger is made possible by a modified 3D printing process. An analytical model is developed to represent the relationship between the soft actuator's air pressure and the finger's deflection angle. Furthermore, analytical modeling of the finger stiffness modulation is presented. Several experiments are conducted to validate the analytical models.