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In adaptive dynamic programming (ADP), the utility function is always completely designed by experience which cannot evaluate system cost very well. A novel adaptive dynamic programming based on genetic algorithms (GAADP) method is proposed with global searching and fast learning speed. First, a normal utility function of ADP was designed according to the error between current states and expected values. Second, genetic algorithms (GAs) were used to search for the optimal parameters of utility function in ADP. Finally, we employed GAADP on an inverted pendulum system control. The simulation experiments indicated that GAADP method can increase the learning speed and easily achieve the balancing state. The learning speed doubled than general ADP method, meanwhile the control performance of successful trials also improved.