Soft pneumatic network actuators have become one of the most promising actuation devices in soft robotics which benefits from their large bending deformation and low input. However, their monotonous bending motion form in two-dimensional (2-D) space keeps them away from wide applications. This paper presents a detailed fabrication method of soft pneumatic network actuators with oblique chambers, to explore their motions in three-dimensional (3-D) space. The design of oblique chambers enables actuators with tunable coupled bending and twisting capabilities, which gives them the possibility to move dexterously in flexible manipulators, to become biologically inspired robots and medical devices. The fabrication process is based on the molding method, including the silicone elastomer preparation, chamber and base parts fabrication, actuator assembly, tubing connections, checks for leaks, and actuator repair. The fabrication method guarantees the rapid manufacturing of a series of actuators with only a few modifications in the molds. The test results show the high quality of the actuators and their prominent bending and twisting capabilities. Experiments of the gripper demonstrate the advantages of the development in adapting to objects with different diameters and providing sufficient friction.