Abstract: In this work, the 24^thand 25^thsolar cycles' periodic characteristics were predicted by using support vector machine(SVM) method and back propagation (BP) neural network method respectively, based upon the data of previous 23 solar cycles. The authors found that both of the methods reach the optimal value after applying the cross validation algorithm, it reveals that the intensity of solar activity in the 25^thsolar cycle will be enhanced comparing with the 24^thsolar cycle in both the SVM and the BP Neural Network prediction; that the sun spot number (SSN) will maintain low value in the valley phase; and the cycle length will be around 10 years in the 25^thsolar cycle. According to the periodic characteristics of the 24^thsolar cycle that was past, there sults from BP Neural Network method prediction are more close to actual situation than that from the SVM. The results indicate that solar activity will enter 25^thsolar cycle in 2020, and will reach the peak in 2025; the amplitude of peak year in the 25^thsolar cycle will be stronger than that in the 24^thsolar cycle.