In recent years, several forecasting methods have been proposed for the analysis of fuzzy time series. Determination of fuzzy relations and establishing interval lengths, which is used in partition of universe of discourse, can be considered as the two of main elements affecting the forecasting performance of these forecasting methods. In the literature, along with the studies in which interval lengths are determined subjectively, algorithms such as genetic algorithms and particle swarm optimization have been utilized. In this study, a new fuzzy time series forecasting method which uses Artificial Bee Colony (ABC) algorithm for the determination of interval lengths for the first time in the literature is proposed. To obtain forecasts, this new method makes use of fuzzy logic relationship tables in determining the fuzzy relations and also uses estimating based on next state (EBN) for training set and master voting (MV) scheme for test set. The new proposed method is applied to three various time series and when compared with the existing methods better results are obtained with regard to both training and test set.