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The integration of variable stiffness materials and structures into soft robots is a popular trend, allowing soft robots to switch between soft and rigid states in different situations. This concept combines the advantages of rigid mechanisms and soft robots, resulting in not only excellent flexibility but also tunable stiffness for high load capacity and fast and precise operation. Here, a stiffness-tunable soft actuator based on wire/fiber jamming structure is proposed, where the fiber-reinforced soft actuator is responsible for the bending motion, and the jamming structure acts as a stiffness-tunable layer controlled by vacuum pressure. The primary design objective of this study is to fabricate a jamming structure with wide-range stiffness, universal adaptability and high dexterity. Thus, the behaviors of wire/fiber jamming structures with different layouts, materials and wire arrangements are analyzed, and a theoretical model is developed to predict the effect of geometric parameters. Experimental characterizations show that the stiffness can be significantly enhanced in the bending direction, while the stiffness is smaller in the torsion direction. Additionally, by integrating Velcro strips into the design, a quick and detachable scheme for the stiffness-tunable soft actuator is achieved. Application examples exhibit high load capacity and good shape adaptability.