In this paper, we study the Navier-Stokes equations with Navier boundary conditions in a bounded domain of R-3. We prove the existence ofweak solution in W-1,W-p(Omega) x L-p(Omega) for 3/2 < p < infinity by using fixed point theorem for the case 3/2 < p < 2. Copyright (C) 2015 John Wiley & Sons, Ltd.