The concept of "prepotency" is introduced in evolution algorithm. The logistic mapping as a simple and powerful device in the chaos theory is combined with the newly proposed prepotency evolution (PE) algorithm to formulate a new genetic algorithm. PE with a population initialized by chaotic numbers is applied to the multiple-layer feed-forward ANN training (PECNN). The logistic mapping ensures the PE starts each time from different initial population never used before. The newly designed PE operator partially includes the crossover and mutation operations implicitly. The proposed algorithm has a higher convergence speed comparing to the conventional GA. During the PE operation the distances between members would become smaller and smaller until all members turning to be almost identical with the potential best minimum being found. It does not waste searching time surrounding the testing minima like the conventional GA and not show symptoms of overfitting to the training set samples. The combination of logistic mapping and PE used in ANN training makes PECNN be able to test lots of minima rapidly and effectively. This greatly enlarges the opportunity to find the global minimum. The proposed algorithm has been testified by prediction of the frequency data of tetrahedral vibration modes (