In this research, a two-phase algorithm based on the artificial neural network (ANN) and a harmony search (HS) algorithm has been developed with the aim of assessing the reliability of structures with implicit limit state functions. The proposed method involves the generation of datasets to be used specifically for training by Finite Element analysis, to establish an ANN model using a proven ANN model in the reliability assessment process as an analyzer for structures, and finally estimate the reliability index and failure probability by using the HS algorithm, without any requirements for the explicit form of limit state function. The proposed algorithm is investigated here, and its accuracy and efficiency are demonstrated by using several numerical examples. The results obtained show that the proposed algorithm gives an appropriate estimate for the assessment of reliability of structures.