We perform a nonperturbative determination of the O(a)-improvement coefficient c(SW) and the critical hopping parameter kappa(c) for N-f=3, 2, and 0 flavor QCD with the (RG) renormalization-group-improved gauge action using the Schrodinger functional method. In order to interpolate c(SW) and kappa(c) as a function of the bare coupling, a wide range of beta from the weak coupling region to the moderately strong coupling points used in large-scale simulations is studied. Corrections at finite lattice size of O(a/L) turned out to be large for the RG-improved gauge action, and hence we make the determination at a size fixed in physical units using a modified improvement condition. This enables us to avoid O(a) scaling violations which would remain in physical observables if c(SW) determined for a fixed lattice size L/a is used in numerical simulations.