The paper presents a Neuro-Fuzzy model to predict the features of the forthcoming sunspot cycles 24 and 25. The sunspot time series were analyzed with the proposed model. It is optimized based on Backpropagation scheme and applied to the yearly smoothed sunspot numbers. The appropriate number of network inputs for the sunspots data series is obtained based on sequential forward search for the Neuro-Fuzzy model. According to the model prediction the maximum amplitudes of the cycles 24 and 25 will occur in the year 2013 and year 2022 with peaks of 101±8 and 90.7±8, respectively. The correlation and error analysis are discussed to ensure the performance of the proposed Neuro-Fuzzy approach as a predictor for sunspot time series. The correlation coefficient between Neuro-Fuzzy model forecasted sunspot number values with the actual ones is 0.96.