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 22na 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.%太阳黑子活动长期预报对航天、通讯、防灾等具有重要的指导意义．针对加权一阶局域法在多步预测时存在累积误差效应，建立了基于相空间重构技术的径向基函数神经网络预测模型．用该模型对第22，23太阳周黑子数平滑月均值进行逐月预报，并与实测值进行比较．结果表明，预报的绝对误差可以控制在15．00以内，平均绝对误差分别为5．47，2．83，相对误差控制在15．00％以内，平均相对误差分别为5．45％，4．60％，验证了该模型在预测太阳黑子数时具有较高的精度．将该预测模型用于第24太阳周黑子数平滑月均值预报，做出了自2009年1月到2019年12月共132个月的黑子数平滑月均值的预报，指出黑子数平滑月均值的最大值为104．77，将出现的时间为2013年1月．
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