Employing a time dependent Ginzburg-Landau type model for nematic liquid crystals in two dimensions, we study the kinetics of nematic ordering in a porous medium following a zero temperature quench from the isotropic phase. We consider various geometrical properties of computer generated model porous media, and compute nematic domain growth laws and scaling functions. Two-dimensional simulation results demonstrate that the growth process slows down dramatically in the presence of a surface anchoring field, which is observed in experiments. Especially, in porous media of a high porosity, we find a nonalgebraic growth of the nematic domain and also a breakdown of the dynamical scaling when the domain size becomes comparable to the average pore diameter. It might be due to the fact that an interconnected and tortuous structure of porous media creates barrier to ordering process.