Long-term prediction of sunspot activity is of great importance for the space activity, communication, disaster prevention and so on. Cumulative error is main shortcoming of weighted one-rank local-region forecasting model for multi-steps prediction of chaotic time series. The radial basis function neural network forecasting model based on phase reconstruction is presented for chaotic time series prediction. The model is applied to the prediction of smoothed monthly mean sunspot numbers for the 22nd and 23rd sun cycles, and compared them with the observations. The results indicate that the mean absolute errors are 5.47 and 2.82, 15 to the maximum in absolute errors, and the mean relative errors are 5.45% and 4.60%, 15.00% to the maximum in relative errors. These results show that this prediction method can be successfully used to predict the smoothed monthly mean sunspot numbers. The predicted maximal smoothed monthly mean sunspot number is 104.77 that will appear in January 2013 for 132 months of cycle 24 from January 2009 to December 2019.