It is shown in this paper that the vacuum configuration of the bilocal field in the global color symmetry model (GCM) can be calculated in the instanton dilute liquid approximation. As only the excitation of Goldstone bosons is taken into account, the relative motion against the vacuum is equivalent to the dynamical mass of a quark. The bilocal field generating the mesons π and σ in the GCM is then determined. With the determined bilocal field and the effective action, the masses and the decay constants of the mesons π and σ, and the decay width of σ→ππ are calculated in the GCM. The calculated results agree with experimental data quite well.