In the paper, we establish a Serrin type criterion for strong solutions to a simplified densitydependent Ericksen--Leslie system modeling incompressible, nematic liquid crystal materials in dimension three. The density may vanish in an open subset of $\Omega$. As a byproduct, we establish the Serrin type criterion for heat flow of harmonic map whose gradients belong to $L^r_xL^s_t$, where $\frac2s+\frac3r\leq1$, for $3<r\leq\infty$.