We have studied the effect of free space nucleon radius on the nuclear matter and slowly rotating neutron-star properties within a relativistic mean-field model with the inclusion of ω-ρ mixing nonlinear term. We use the same density-dependent radius as in our previous work. However, in the present work, we utilize the parameter sets with more proper symmetric nuclear matter (SNM) predictions for a number of different nucleon radii. To this end, the isoscalar parameters in each parameter set and the cutoff parameter β are adjusted by fitting the corresponding SNM properties at subsaturation density to the prediction of IUFSU parameter set. Our results show that the assumption of composite nucleons with free space radius r≤0.83 fm is still compatible with the currently acceptable nuclear matter (NM) properties beyond the saturation density. We have also found that the effect of free space nucleon radius could be imprinted in the radius, moment of inertia, and crust properties of the slowly rotating neutron star.