The influence of the counterion size is investigated in the mixed counterion systems of the salt-free polyelectrolyte solution in a cylindrical cell model. The mixtures of two species of the counterion having the same valence and different size are simulated systematically by means of the Monte Carlo method in the primitive model of the rodlike polyelectrolyte solution. The results of the free fractions and the selectivity coefficients are compared with the numerical solutions of the Poisson-Boltzmann equation. The observed differences between both methods are explained in terms of the ion-ion correlations and the effect of finite ion size.