  For any $r$-uniform hypergraph $\mathcal{H}$ with $m$ ($\geq 2$) edges, let
$P(\mathcal{H},k)$ and $P_l(\mathcal{H},k)$ be the chromatic polynomial and the
list-color function of $\mathcal{H}$ respectively, and let $\rho(\mathcal{H})$
denote the minimum value of $|e\setminus e'|$ among all pairs of distinct edges
$e,e'$ in $\mathcal{H}$. We will show that if $r\ge3$, $\rho(\mathcal{H})\ge 2$
and $m\ge \frac{\rho(\mathcal{H})^3}2+1$, then
$P_l(\mathcal{H},k)=P(\mathcal{H},k)$ holds for all integers $k\geq
\frac{2.4(m-1)}{\rho(\mathcal{H})\log(m-1)}$.
