By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equatios in arbitrary three dimensional domain with uniformlyC 3 boundary, under the assumption that |a| L 2(.) + |f| L 1(0,.;L 2(.)) or |.a| L 2(.) + |f| L 2(0,.;L 2(.)) small or viscosityv large. Herea is a given initial velocity andf is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.