Local minimum incorporated with premature saturation and slower convergence limits the performance of the Simple Genetic Algorithm based Neural Network (SGA-NN) algorithm. When the network reaches in local minima, the weights of the neural network become idle. To overcome this premature saturation and slow convergence a new neuro-genetic system named Apical Dominance based Genetic Algorithm based Neural Network (ADGA-NN) is proposed in this research work. As ‘Apical Dominance’ is a natural genetic event in plants, this algorithm may accelerate the training by updating the stationary weights of the neural network. ADGA-NN is experimented on five actual world's classification problems which are breast cancer, glass, Australian credit card, heart disease and thyroid problem. ADGA-NN surpasses SGA-NN concerning convergence rate and generalization capability.