Considering the scenarios that emergencies damage the service abilities of some emergency facilities. Service quantities are defined, among emergency facilities and demand points, by using maximum and minimum critical coverage distance. An emergency facility location model is established within the objective to maximizing overall service quality expectation while ensure minimum service quality and quantity requirements. In order to solve this model, an efficient algorithm is designed based on simulated annealing algorithm. Numerical experiments on the number of emergency facilities, critical coverage range, minimum service quality are analyzed, these results show it is useful for decision of emergency facility location both the model and algorithm proposed in this paper.