When a polymer network is exposed to a suitable solvent, the migration of solvent molecules into the network will cause volumetric deformation, known as swelling, but more importantly forms a mixture that is known as a polymeric gel. Despite numerous potential applications, many aspects of the coupled diffusion-deformation behavior in polymeric gels have not yet been thoroughly investigated. Here, we focus our attention on the coupled deformation-diffusion response of fiber-reinforced polymeric gels. The presence of embedded fibers in a swellable polymer matrix leads to anisotropy in the overall behavior. In order to capture this response, we have developed a constitutive model for fiber-reinforced polymeric gels, that explicitly takes into account anisotropy in both the mechanical and diffusive behavior. The constitutive model is implemented as user element subroutine (UEL) in the commercial finite element software package Abaqus/Standard. Numerical simulations are performed to show the behavior of the model, and qualitative comparisons are made to experiments of a soft robotic gripper.