Summary: We establish a blow up criterion for the short time classical solution of the nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three. More precisely, \(0<T_*<+\infty\) is the maximal time interval iff (i) for \(n=3\), \(|\omega|+|\nabla d|^2\notin L^1_tL^\infty_x(\mathbb{R}^3\times[0,T_*])\); and (ii) for \(n=2\), \(|\nabla d|^2\notin L_t^1L_x^\infty(\mathbb{R}^2\times[0,T_*])\).