Brain Computer interface (BCI) shown enormous ability to advance the human way of life. Furthermore its application is also targeting the disabled ones. In this research, we have implemented a new approach to classify EEG signals more efficiently. The dataset used for this purpose is from BCI competition-II 2003 named Graz database. Initial processing of the EEG signals has been carried out on 2 electrodes named C3 & C4; after that the bi-orthogonal wavelet coefficients, Welench Power Spectral Density estimates and the average power were used as a feature set for classification. We have given a relative study of currently used classification algorithms along with a new approach for classification i.e. Self-organizing maps (SOM) based neural network technique. It is used to classify the feature vector obtain from the EEG dataset, into their corresponding classes belong to left/right hand movements. Algorithms have been implemented on both unprocessed features and processed reduced feature sets. Principal component Analysis (PCA) has been used for feature reduction. Measured data revealed that the maximum classification accuracy of 84.17 on PCA implemented reduce feature set has been achieved using SOM based classifier. Furthermore, the classification accuracy has been increased about 2 by simply using bi-orthogonal Wavelet transform rather than Daubechies wavelet transform. © 2014 IEEE.