  We establish some interior regularity criterions of suitable weak solutions
for the 3-D Navier-Stokes equations, which allow the vertical part of the
velocity to be large under the local scaling invariant norm. As an application,
we improve Ladyzhenskaya-Prodi-Serrin's criterion and
Escauriza-Seregin-\v{S}ver\'{a}k's criterion. We also show that if weak
solution $u$ satisfies $$ \|u(\cdot,t)\|_{L^p}\leq C(-t)^{\frac {3-p}{2p}} $$
for some $3<p<\infty$, then the number of singular points is finite.
