Stimuli-responsive polymeric gels are capable of undergoing large deformation due to change in environmental stimuli like temperature, pH, ionic strength, electric field, and light. The unique swelling and shrinking properties of gels make them a promising class of materials as sensors and actuators in a wide range of fields, such as tissue engineering, drug delivery, and soft robotics. Hydrogels can be shaped into various structures based on their intended use. However, the traditional fabrication approach involves the use of layered structures, which greatly restricts its potential due to the uneven distribution of force at the interfaces. To overcome this limitation, a mono-component functionally graded material system is proposed. A model based on coupled swelling and deformation mechanisms is developed to predict the folding behaviour of functionally graded (FG) hydrogel thin films. The gradation is achieved by changing the cross-link density, diffusion coefficient, and Flory–Huggins interaction parameter through the thickness of the film, either linearly or non-linearly. In this context, two different folding scenarios are simulated, one when the film is immersed in a solvent bath, while the other explores folding the film with only one side in contact with the solvent outside the bath. Each case provides unique insights into the film's response under different conditions. The results obtained using this model are compared with experiments for a functionally graded chitosan-water system. Further, the developed model is used to design different underwater grippers. Considering the number of variables involved in designing a functionally graded system, the developed model, with a detailed explanation of the folding mechanism, can serve as a design guideline for developing such solvent-responsive systems