In this paper, we prove the L-p-L-q maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. The result was first stated by Solonnikov [ 17], but he assumed that p = q > 3 and considered only the finite time interval case. In this paper, we consider not only the case: 1 < P, q < infinity but also the infinite time interval case. Especially, we obtain the L-p-L-q maximal regularity theorem with exponential stability on the infinite time interval.