  In this paper, we study the global regularity of strong solution to the
Cauchy problem of 3D incompressible Navier-Stokes equations with large data and
non-zero force. We prove that the strong solution exists globally for $\nabla
u\in L^{\alpha}\left( 0,T,L^{2}\left( \Omega\right) \right) $ with
$2\leq\alpha\leq4$.
