Abstract: As a kind of new smart materials, hydrogel has a special chemomechanical coupling effect. By using the functionally graded material, the adaptability and controllability of the hydrogel can be improved distinctly. In this analysis, the crosslink density of the hydrogel is assumed to be a power-law function of the radial position. By employing the general multi-field coupling large deformation theory and the Flory-Huggins free energy function, the governing equations of the functionally graded spherical hydrogel (FGSH) undergoing the spherically symmetric deformation are developed. The theoretical analysis of the swelling behavior accompanying the inhomogeneous large deformation is presented for the FGSH when subjected to the internal pressure and the prescribed chemical potential. Numerical results show that both the internal pressure-internal radius curve and the internal pressure-radial stretch curve exhibit a stable region and an unstable region, which means that if the internal pressure exceeds a certain critical value, the instability will occur and the hydrogel will finally be damaged. The critical value of the internal pressure increases with the increasing of gradient index. It is shown that the material parameters, such as gradient index, the interaction parameter between the polymer network and the solvent, the cross-link density and the volume of the solvent molecular, and the environmental chemical potential have a significant effect on the swelling behavior of the FGSH. If the internal pressure is fixed, the radial displacement of FGSH at the internal surface is nearly linear with respect to the gradient index, while it appears obvious nonlinear to other parameters. The investigation is helpful to realize the precise control of the hydrogel-based smart structures and devices under the complex environments.