In this paper, we propose the Priority Facility Location Problem with Outliers (PFLPO), which is a generalization of both the Facility Location Problem with Outliers (FLPO) and Priority Facility Location Problem (PFLP). As our main contribution, we use the technique of primal-dual to provide a 3-approximation algorithm for the PFLPO. We also give two heuristic algorithms. One of them is a greedy-based algorithm and the other is a local search algorithm. Moreover, we compare the experimental results of all the proposed algorithms in order to illustrate their performance.