We perform a nonperturbative determination of the O(a)-improvement coefficient c&lt
inf&gt
SW&lt
/inf&gt
for the Wilson quark action in three-flavor QCD with the plaquette gauge action. Numerical simulations are carried out in a range of β = 12.0-5.2 on a single lattice size of 8&lt
sup&gt
3&lt
/sup&gt
× 16 employing the Schrödinger functional setup of lattice QCD. As our main result, we obtain an interpolation formula for c&lt
inf&gt
SW&lt
/inf&gt
and the critical hopping parameter K&lt
inf&gt
c&lt
/inf&gt
as a function of the bare coupling. This enables us to remove the O(a) scaling violation from physical observables in future numerical simulation in the wide range of β. Our analysis with a perturbatively modified improvement condition for c&lt
inf&gt
SW&lt
/inf&gt
suggests that finite volume effects in c&lt
inf&gt
SW&lt
/inf&gt
are not large on the 8&lt
sup&gt
3&lt
/sup&gt
× 16 lattice. We investigate N&lt
inf&gt
f&lt
/inf&gt
dependence of c&lt
inf&gt
SW&lt
/inf&gt
by additional simulations for N&lt
inf&gt
f&lt
/inf&gt
= 4, 2, and 0 at β = 9.6. As a preparatory step for this study, we also determine c&lt
inf&gt
SW&lt
/inf&gt
in two-flavor QCD at β = 5.2. At this β, several groups have carried out large-scale calculations of the hadron spectrum, while no systematic determination of c &lt
inf&gt
SW&lt
/inf&gt
has been performed. ©2005 The American Physical Society.