In this paper we discuss how a Gesture Recognition system for Alphabetical Hand Gestures is built. The main motive was to develop a system that can simplify the way humans interact with computers. The system is designed using the Support Vector Machine (SVM) Classifier which is widely used for classification and regression testing. SVM training algorithm builds a model that predicts whether a new example falls into one category or other. And the SVM classifier learns from the data points in examples when they are classified belonging to their respective categories.