Complexation between the beta-lactoglobulin and a weak acid polyelectrolyte (PE) has been studied using Monte Carlo simulations. Different coarse-grained models were used to represent the system, and two different acidic constants were used on the PE model. The protein-PE interaction is quantified considering the average PE monomers adsorbed on the protein as a function of pH. A maximum in the interaction between macromolecules was found, which is explained as a function of the titration behavior of the beta-lactoglobuline and weak PE. We also found that there was a direct relation between the pH range of monomers adsorbed and the change on dissociation profile of the protein and weak PE compared to isolated conditions. The complexation of protein PE increased both the dissociation degree of the PE chain and the protein net charge. This benefits the monomer adsorption on the protein surface.