ANFIS is an artificial intelligence technique which is composed of a combination of artificial neural networks and fuzzy inference system. Due to its structure, it is used in modeling and identifying numerous systems in various fields. The training process of ANFIS is important to obtain effective results with it. So, a successful training algorithm should be used. In this study, the ANFIS is trained by using ABC algorithm for the solution of the real-world problem. For this purpose, the number of foreign visitors coming to Turkey from the USA, Germany, Bulgaria, France, Georgia, the Netherlands, England, Iran and Russia is estimated. In addition, total number of visitors coming to Turkey is also predicted. In applications, 150 months of data between July 2002 and December 2014 are utilized and a time series is created using these data. The results obtained using ABC algorithm are compared with GA, DE, HS and PSO. As a conclusion, it is seen that the results obtained using ABC algorithm for estimation of number of foreign visitors are more successful than other optimization methods.