Using the "post-processing" technique, we explore the role of the convective overshooting on the production of s-nuclei in stellar models of different initial mass and metallicity (M_ZAMS_ in the range 15-25M_{sun}_ Z in the range 10^-4^-0.02), considering a range of values for the parameter f, which determines the overall efficiency of convective overshooting. We find enhancements in the production of s-nuclei until a factor ~6 (measured as the average overproduction factor of the 6 s-only nuclear species with 60<A<90) in all our models of different initial mass and metallicity having f in the range 0.01-0.035 (i.e. models with overshooting), compared to the production obtained with "no-overshooting" models (i.e. models having the same initial mass and metallicity but f=10^-5^). Moreover the results indicate that the link between the overshooting parameter f and the s-process efficiency is essentially monotonic in all our models of different initial mass and metallicity. Also evident is the higher s-process efficiency when, for a given f value, we progressively increase both the mass of the models from 15 to 25M_{sun}_ and the Z value from 10^-4^ to 0.02.