Among the central nervous system (neurological) disorders, epilepsy is considered to be a dangerous and chronic disorder that causes recurring seizures, showing unusual behaviour for some period of time, shaking of hands and legs, loss of sensation and awareness. It occurs when electrical activities in the brain become abnormal. The test performed in order to detect epileptic seizures is known as electroencephalograph (EEG) signal test which is conducted by analysing the electrical impulses in the brain. The manual identification process of EEG brain signals is time consuming and a laborious task. So the neurologists may sometimes give a varying result which may affect the performance of detecting epileptic seizures. The combination of manual identification of the signal and machine learning technique will be able to provide a correct result in a confusion situation reducing analytic and therapeutic errors that are unavoidable in human clinical practice. The existing approaches of detection of epileptic seizures cannot correctly train their network if the size of the dataset is very large thus obtaining lower classification accuracy. An optimized neural network technique is proposed in this work for automatic detection of Epileptic seizure using EEG signals of the brain. The EEG signals are used for feature extraction by applying Discrete Wavelet Transform (DWT). Using the extracted features, input samples are created and then fed to a hybrid model which is a combination of self-organizing neural network (SONN) and multilayer perceptron (MLP) trained with a genetic algorithm (GA). This model acts as a classifier for detecting Epileptic seizures by classifying the samples into two classes namely Non-Epileptic and Epileptic class. Clustering is performed first for the large dataset samples using SONN and for each cluster, an MLP-GA network is used to train the samples belonging to the same cluster. Performing clustering helps to correctly train the MLP networks for obtaining high classification accuracy. GA has been specifically chosen as a learning algorithm instead of Backpropagation (BP) algorithm for MLP because GA can find the global minima thus solving the local minima problem faced by BP algorithm. The performance measures are evaluated thereby achieving precision value of 98%, recall value of 100%, F1 score value of 98.99% and an overall accuracy of 99.2%. The proposed hybrid method using SONN and MLP-GA has more potential to classify the EEG signals.