Early crack detection in structures prevents the occurrence of damage. Therefore, there is challenge in the literature to provide efficient methods in the field of structural health monitoring. A lot of researches that have been done on the crack identification in structures, are based on the models which ignore crack closure effects that make a significant error in the crack identification. Since it is more difficult to identify breathing crack than other damages, the purpose of this research is providing an efficient algorithm to identify breathing crack in beam-type structures which are important elements in various types of structures. In order to calculate natural frequencies of the beam accurately, in this research the fatigue crack model is used, which considers crack as breathing one with opening and closing behaviour. Then the problem of identifying crack parameters (location and depth of the crack) is defined as an optimization problem with the aim of minimizing the differences between natural frequencies calculated by the model and measured natural frequencies. In order to choose an appropriate algorithm to identify breathing crack, algorithms among various meta-heuristic algorithms are selected, which is able to identify the crack using only two natural frequencies. Regarding the surveys conducted, the optimization problem is solved using cat swarm optimization (CSO) algorithm. Moreover, in order to validate, the results are obtained for different crack parameters, have been compared with those of experimental tests. The results indicate that the proposed method has good accuracy