In this paper we study the uncapacitated facility location problem in the model of differential privacy (DP) with uniform facility cost. Specifically, we first show that, under the hierarchically well-separated tree (HST) metrics and the super-set output setting that was introduced in Gupta et. al., there is an $ε$-DP algorithm that achieves an $O(\frac{1}ε)$(expected multiplicative) approximation ratio; this implies an $O(\frac{\log n}ε)$ approximation ratio for the general metric case, where $n$ is the size of the input metric. These bounds improve the best-known results given by Gupta et. al. In particular, our approximation ratio for HST-metrics is independent of $n$, and the ratio for general metrics is independent of the aspect ratio of the input metric. On the negative side, we show that the approximation ratio of any $ε$-DP algorithm is lower bounded by $Ω(\frac{1}{\sqrtε})$, even for instances on HST metrics with uniform facility cost, under the super-set output setting. The lower bound shows that the dependence of the approximation ratio for HST metrics on $ε$ can not be removed or greatly improved. Our novel methods and techniques for both the upper and lower bound may find additional applications.