Last few decades have witnessed the use of artificial neural networks (ANN) in many real-world applications and have offered an attractive paradigm for a broad range of adaptive complex systems. In recent years ANN have enjoyed a great deal of success and have proven useful in wide variety pattern recognition or feature extraction tasks. Examples include optical character recognition, speech recognition and adaptive control to name a few. To keep the pace with its huge demand in diversified application areas, many different kinds of ANN architecture and learning types have been proposed by the researchers to meet varying needs. A novel hybrid learning approach for the training of a feed-forward ANN has been proposed in this thesis. The approach combines evolutionary algorithms with matrix solution methods such as singular value decomposition, Gram-Schmidt etc., to achieve optimum weights for hidden and output layers. The proposed hybrid method is to apply evolutionary algorithm in the first layer and least square method (LS) in the second layer of the ANN. The methodology also finds optimum number of hidden neurons using a hierarchical combination methodology structure for weights and architecture. A learning algorithm has many facets that can make a learning algorithm good for a particular application area. Often there are trade offs between classification accuracy and time complexity, nevertheless, the problem of memory complexity remains. This research explores all the different facets of the proposed new algorithm in terms of classification accuracy, convergence property, generalization ability, time and memory complexity.