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In order to manage the grid resources more effectively and provide a more suitable task scheduling strategy, the prediction information of grid resources is necessary in the grid system. In this study, support vector regression (SVR), which is a novel and effective regression algorithm, is applied to grid resource prediction. In order to build an effective SVR model, SVR's parameters must be selected carefully. Therefore, we develop a genetic algorithm-based SVR (GA-SVR) model that can automatically determine the optimal parameters of SVR with higher predictive accuracy and generalization ability simultaneously. This study pioneered on employing genetic algorithm to optimize the parameters of SVR for grid resource prediction. The performance of the hybrid model (GA-SVR), the back-propagation neural network (BPNN) and traditional SVR model whose parameters are obtained by trial-and-error procedure (T-SVR) have been compared with benchmark data set. Experimental results demonstrate that GA-SVR model works better than the other two models.