This paper proposes a new forecasting model based on the neural networkwith weighted fuzzy membership functions (NEWFM) concerning forecastingof turning points in the business cycle by the composite index. NEWFM is anew model of neural networks to improve forecasting accuracy by using selfadaptive weighted fuzzy membership functions. The locations and weights ofthe membership functions are adaptively trained, and then the fuzzymembership functions are combined by the bounded sum. To simplify theforecasting processes, the non-overlap area distribution measurementmethod is applied to select important features by deleting less importantinputs. The implementation of the NEWFM demonstrates an excellentcapability in the field of business cycle analysis.