This paper proposes the forecasting model for the fuzzy time series based on the improvement of the background data and fuzzy relationship (IFTC). This algorithm is built based on the fuzzy cluster analysis which the suitable number of clusters for series is considered. The problem of interpolating data according to fuzzy relationships of time series in the trapezoidal fuzzy number is also established. The proposed model is illustrated step by step by a numerical example and effectively implemented by the Matlab procedure. The IFCT has advantages in comparing to other models via the several indexes such as the MAE, MAPE and MSE with the Enrollment dataset.