This paper proposes a new model to interpolate time series and forecast it effectively for the future. The important contribution of this study is the combination of optimal techniques for fuzzy clustering problem using genetic algorithm and forecasting model for fuzzy time series. Firstly, the proposed model finds the suitable number of clusters for a series and optimizes the clustering problem by the genetic algorithm using the improved Davies and Bouldin index as the objective function. Secondly, the study gives the method to establish the fuzzy relationship of each element to the established clusters. Finally, the developed model establishes the rule to forecast for the future. The steps of the proposed model are presented clearly and illustrated by the numerical example. Furthermore, it has been realized positively by the established MATLAB procedure. Performing for a lot of series (3007 series) with the differences about characteristics and areas, the new model has shown the significant performance in comparison with the existing models via some parameters to evaluate the built model. In addition, we also present an application of the proposed model in forecasting the COVID-19 victims in Vietnam that it can perform similarly for other countries. The numerical examples and application show potential in the forecasting area of this research.