Surface roughening has been extensively studied in many fields of science and technology. In order to investigate the influence of imperfection of the randomly diluted lattices on dynamic scaling behavior of the surfaces, the etching model growing on diluted squares is simulated by kinetic Monte Carlo (KMC) simulation. It is found that although the scaling behavior of the etching model can be affected by imperfections of the randomly diluted lattices, the roughness and the growth exponent are larger than those of the growth on perfect squares. The scaling behavior still satisfies the Family-Vicsek dynamic scaling. In addition, the finite system size effect of the randomly diluted lattice is also calculated and analyzed.