Alginate-based hydrogel is widely used as bio-ink in 3D bioprinting. For producing the bio-ink and stabilizing the polymer network, the hydrogel shall undergo a gelation process which can be obtained by adding an ionic cross-linker agent, such as Calcium ions for alginate. The diffusion of the crosslinker in the alginate stabilizes the polymeric network thanks to the reaction of Calcium ions with alginate monomers. This work presents a reaction-diffusion computational model of the gelation mechanism in alginate hydrogels. The coupled chemical system is solved using finite element discretizations considering the inhomogeneous evolution of the gelation process in time and space.