Adaptive Neuro Fuzzy Inference System (ANFIS) is an adaptive network that can use the computation and learning abilities of artificial neural network together with the inference feature of fuzzy logic. The ANFIS system, which is used in the solution of many problems such as classification and estimation of deep learning applications, meets the needs in many different areas such as modeling, control, and parameter estimation. In recent years, heuristic methods have been used for the training of this network, which requires initial and result parameters by its structure. Moth-Flame Optimization Algorithm (MFO) is one of the current heuristic methods modeled by the influence of the spiral movement of the moths towards the light source. In this study, the MFO algorithm was used for the first time for the optimization of initial and result parameters in the ANFIS system. In the determination of parameters, nonlinear system identification, time series estimation, classification problems were tried to be solved. When the results obtained for the ANFIS trained with the known heuristic methods such as Particle Swarm Optimization(PSO), Genetic Algorithm(GA) and Whale Optimization Algorithm(WOA) and the results of ANFIS trained by the MFO were examined, it was observed that the MFO had lower error values.