Two new hybrid algorithms are proposed to improve the performances of the meta-heuristic optimization algorithms, namely the Grey Wolf Optimizer (GWO) and Shuffled Frog Leaping Algorithm (SFLA). Firstly, it advances the hierarchy and position updating of the mathematical model of GWO, and then the SGWO algorithm is proposed based on the advantages of SFLA and GWO. It not only improves the ability of local search, but also speeds up the global convergence. Secondly, the SGWOD algorithm based on SGWO is proposed by using the benefit of differential evolution strategy. Through the experiments of the 29 benchmark functions, which are composed of the functions of unimodal, multimodal, fixed-dimension and composite multimodal, the performances of the new algorithms are better than that of GWO, SFLA and GWO-DE, and they greatly balances the exploration and exploitation. The proposed SGWO and SGWOD algorithms are also applied to the prediction model based on the neural network. Experimental results show the usefulness for forecasting the power daily load.