Origami metamaterial has gradually shown its potential in the fields of science and engineering due to its unique mechanical behaviors. Since hydrogel shows a positive volume change when absorbing water, it provides a new design strategy for actively deformed origami metamaterials composed of normal material framework and active hydrogel layer. In this paper, we proposed three synergistic mechanical designs with positive/negative/zero tunable swelling deformation by adjusting the opening direction of the circular holes. The deformation behaviors of the origami metamaterials manufactured by a multi-material 3D printer were qualitatively and quantitatively characterized and demonstrated, using finite element analysis, experimental test and theoretical method. The results indicate that the origami metamaterials present significant tunable swelling behaviors, which can be customized by adjusting the lattice microstructure geometry parameters. Utilizing the origami metamaterials, cylindrical shell and box structures with tunable swelling behavior were designed. Additionally, the hydrogel-driven actuator based on the origami metamaterials was manufactured to pull/drag an underwater object. Since the tunable swelling behaviors are not related to scale, these hydrogel-driven origami metamaterials can be applied to the design of reconfigurable and programmable devices on the macro and micro scale and possess promising potential for wide applications in bioelectronics and biological tissue engineering.