For soft grippers to be applied in atypical industrial environments, they must conform to an object’s exterior shape and momentarily change their stiffness. However, many of the existing grippers have limitations with respect to these functions: they grasp an object with only a single curvature and a fixed stiffness. Consequently, those constraints limit the stability of grasping and the applications. This paper introduces a new multicurvature, variable-stiffness soft gripper. Inspired by the human phalanx and combining the phalanx structure and particle jamming, this work guarantees the required grasping functions. Unlike the existing soft pneumatic grippers with one curvature and one stiffness, this work tries to divide the pressurized actuating region into three parts to generate multiple curvatures for a gripper finger, enabling the gripper to increase its degrees of freedom. Furthermore, to prevent stiffness loss at an unpressurized segment, this work combines divided actuation and the variable-stiffness capability, which guarantee successful grasping actions. In summary, this gripper generates multiple grasping curvatures with the proper stiffness, enhancing its dexterity. This work introduces the new soft gripper’s design, analytical modeling, and fabrication method and verifies the analytic model by comparing it with FEM simulations and experimental results.