This article proposes a new fuzzy time series (NFTS) model that can interpolate historical data to forecast effectively for the future. In this model, after normalizing original data, we establish the automatic algorithm to determine the suitable number of clusters and to find the fuzzy relationships of each element in series to the established clusters. A principle for forecasting is also proposed from these established fuzzy relationships. The convergence of the proposed algorithm is proven by theory and shown by the numerical examples. The calculation of the proposed model can be performed conveniently and efficiently by a complete Matlab procedure. Comparing with many existing models from a lot of well-known data sets with various scales and characteristics, NFTS model has shown prominent advantages.