In traditional covering problem, covering levelof receiving the services is independent ofdistances between nodes and facilities. However in gradual covering location problem (GCLP) the covering objective depends on the distance of customers from the service centers. Hence increasing incustomer-facility distances will results in decreasing the covering level. In most of covering problems, researchers only consider the distance factor. However; in the real word there are some other important elements such as population, availability, distance and etc. which affect the location of service center. Increasing the number of demand nodes and criteria’s will result in increasing the nodes evaluating computational time and inconsistency rate. This paper proposes a combined Simulated annealing (SA) and Artificial Neural Network (ANN) approaches to solve the multi criteria GCLP.In presence of few nodes; score of nodes are calculated usingAnalytic Hierarchy Process (AHP) method. Moreover by increasingthe number of nodes the score of every node will be calculated using ANNinstead of AHP. Statistical test of signed rank test shows that there is not a significant difference between the result of ANN and AHP methods. The comparison results between the exact solution method and the proposed algorithm confirms the efficiency of the proposed solution approach.