In this paper, we propose a hybrid genetic algorithm based on variable grouping and uniform design for global optimization problems, a function formula based grouping (FBG) strategy is adopted to classify the separable variables into different groups and put the interactive variables into the same group. In this way, the problem considered can be changed into several lower dimension sub-problems. The solution can be more easily obtained by simultaneously solving these sub-problems. Then, an efficient crossover operator is designed by using a specific uniform design method. When we have no prior knowledge on global optimal solution, this crossover operator has more possibility to find high quality solutions. Furthermore, in order to enhance the diversity and efficient explore the search space, an adapted mutation operator is design to adaptively adjust the search scope, and a local search scheme is proposed to speed up the search. By integrating all these schemes, a hybrid genetic algorithm is proposed for global optimization problems. Finally, the experiments are conducted on widely used benchmarks and the results indicate the proposed algorithm is efficient and effective.