We present a covolume method for the modified Stokes problem using the simplest approximation spaces, Q(1)-P-0. This scheme turns out the stabilized covolume method for the Stokes problem. We prove that the covolume method in this paper has a unique solution and O(h) convergence order in H-1 semi-norm for the velocity and in L-2 norm the pressure approximants, respectively. We also present numerical results corresponding to our analysis. (C) 2001 Elsevier Science B.V. All rights reserved.