In this paper, we establish a criterion for the breakdown of local in time classical solutions to the incompressible nematic liquid crystal system with zero viscosity in dimensions three. More precisely, let $$T_{*}$$ T ∗ be the maximal existence time of the local classical solution, then $$T_{*}<+\infty $$ T ∗ < + ∞ if and only if $$\begin{aligned} \int \limits _{0}^{T_{*}}\frac{\Vert \nabla u\Vert _{\dot{B}^{0}_{\infty ,\infty }}+\Vert \nabla d\Vert _{\dot{B}^{0}_{\infty ,\infty }}^{2}}{\sqrt{1+\ln (e+\Vert \nabla u\Vert _{\dot{B}^{0}_{\infty ,\infty }} +\Vert \nabla d\Vert _{\dot{B}^{0}_{\infty ,\infty }})}}\hbox {d}t=\infty . \end{aligned}$$ ∫ 0 T ∗ ‖ ∇ u ‖ B ˙ ∞ , ∞ 0 + ‖ ∇ d ‖ B ˙ ∞ , ∞ 0 2 1 + ln ( e + ‖ ∇ u ‖ B ˙ ∞ , ∞ 0 + ‖ ∇ d ‖ B ˙ ∞ , ∞ 0 ) d t = ∞ . The result can be regarded as a corresponding logarithmical blow-up criterion in Huang and Wang (Commun. Partial Differ. Equ. 37:875–884, 2012) for the nematic liquid crystal system with zero viscosity.