Location Set Covering Problem (LSCP) is a traditional problem in the location literature. LSCP is used in locating fire stations, computer networks, and many other service facilities. This paper proposes a covering problem with variable radii. In this problem, the cost to establish a facility is a monotonically increasing function of distance to the farthest covered node by the facility. The problem is to cover all the demand nodes with the least total cost, where the number, location, coverage radii and the assignment of demands to facilities should be determined. Here, the travel times between nodes are considered to be fuzzy variables. A combination of fuzzy simulation and Simulated Annealing (SA) is proposed in order to solve this problem and a numerical example is given for validation of the proposed model.