We present a novel genetic algorithm and least square (GALS) based hybrid learning approach for the training of an artificial neural network (ANN). The approach combines evolutionary algorithms with matrix solution methods such as Gram-Schmidt, SVD, etc., to adjust weights for hidden and output layers. Our hybrid method (GALS) incorporates the evolutionary algorithm (EA) in the first layer and the least square method (LS) in the second layer of the ANN. In the proposed approach, a two-layer network is considered, the hidden layer weights are evolved using an evolutionary algorithm and the output layer weights are calculated using a linear least square method. When a certain number of generation or error goals in terms of RMS error is reached, the training is stopped. We start training with a small number of hidden neurons and then the number is increased gradually in an incremental process. The proposed algorithm was implemented and many experiments were conducted on benchmark data sets such as XOR, 10-bit odd parity, handwritten segmented characters recognition, breast cancer diagnosis and heart disease data. The experimental results showed very promising results when compared with other existing evolutionary and error back propagation (EBP) algorithms in classification rate and time complexity.