A new double elite coevolutionary genetic algorithm (DECGA) is proposed to avoid the premature convergence and low speed of convergence, based on the elite strategy and the concept of coevolutionary. In the DECGA, the two different and high fitness individuals (elite individuals) are selected as the core of the evolutionary operation, and the team members are selected by the different evaluation functions to form two teams through these two elite individuals. The two sub-populations can balance the capability of exploration and exploitation by the different evolutionary strategies. Theoretical analysis proves that the algorithm converges to the global optimization solution. Tests on the functions show that the algorithm can find the global optimal solution for most test functions, and it can also maintain the population diversity to a certain range. Compared with the existing algorithms, DECGA has a higher performance in precision of convergence and search efficiency.