  In this paper, we investigate regularity criterion for the solution of the
nematic liquid crystal flows in dimension three and two. We prove the solution
$(u,d)$ is smooth up to time $T$ provided that there exists a positive constant
$\varepsilon_{0}>0$ such that (i) for n=3, |(u,\nabla
d)|_{L^{\infty}(0,T;\dot{B}^{-1}_{\infty,\infty})}\leq \varepsilon_{0}, and
(ii) for $n=2$, |\nabla d|_{L^{\infty}(0,T;\dot{B}^{-1}_{\infty,\infty})}\leq
\varepsilon_{0}.
