The purpose of this article was to theoretically study the non-Fickian moisture absorption process in vegetable-fiber-reinforced polymer composites using a Langmuir-type model. Here, the focus was on evaluating the effect of the water layer thickness that surrounds the composite during the water migration process. The solutions of the governing equations were obtained using the finite volume method, considering constant thermophysical properties and non-deformable material. The results for the local and average moisture content and concentration, gradient values, and the transient rates of the free and bound (water) molecules in the process were presented and analyzed. It was observed that the water layer thickness strongly influenced the water absorption kinetics, the moisture content gradient values, and the equilibrium moisture content inside the material. It is envisaged that this new approach will contribute to better interpretation of experimental data and a better understanding of the physical phenomenon of water absorption, which directly affects the properties of composite materials.