Pneumatic soft actuators possess relatively fast response, inherent high flexibility, and achieve extraordinary shape morphing under large deformations. Conventionally, the entire body of soft pneumatic robots needs to be designed for specific applications. Herein, a soft pneumatic actuator design with structured fabrics as actuator skins, which has high bending stiffness variation that can accomplish multiple tasks and different deformation modes in a single body, is proposed. By adjusting the structured skin, the developed soft actuator can be tailored to achieve various deformations. It is experimentally shown that the bending stiffness of the actuator can be adjusted from 108 to 5654 N m−1. The blocking force of the actuator in bending is comparable with that of conventional fabric‐reinforced pneumatic actuators, while the actuator skins are reusable and programmable. In application, the actuators are used to construct a bionic soft gripper with multiple degrees of freedom. By switching between three grasping modes, the gripper successfully fulfills a series of tasks including lifting weights up to 1 kg and grasping objects ranging from a grain of grape to a large iron basin. This work opens up an avenue for designing structured skins for pneumatic robots with programmable deformation modes and versatile functions.