The purpose of this study is to delete the redundant connections of hierarchical neural network constructed for solving pattern recognition problem with images. The performance of neural network changes depending on the number of hidden units. For example, a lot of hidden units cause the over-fitting problem and make it difficult to understand the role of hidden units. In order to diminish the redundant connections, we propose the connection elimination method by using genetic algorithm. Firstly, walsh-hadamard transform is applied to images for feature extraction. Secondly, neural network is trained with extracted features based on back-propagation algorithm. Finally, redundant connections are eliminated by optimization processing with genetic algorithm. In order to show the effectiveness of the proposed method, computer simulation is performed for face recognition examples. From the simulation results, it was confirmed that our proposed method was useful for eliminating redundant connections of neural network, maintaining recognition performance at high level.