Indiana University-Purdue University Indianapolis (IUPUI) / Emotions are essential for our existence, as they exert great influence on the mental health of people. Speech is the most powerful mode to communicate. It controls our intentions and emotions. Over the past years many researchers worked hard to recognize emotion from speech samples. Many systems have been proposed to make the Speech Emotion Recognition (SER) process more correct and accurate. This thesis research discusses the design of speech emotion recognition system implementing a comparatively new method, i-vector model. I-vector model has found much success in the areas of speaker identification, speech recognition, and language identification. But it has not been much explored in recognition of emotion. In this research, i-vector model was implemented in processing extracted features for speech representation. Two different classification schemes were designed using two different classifiers - Gaussian Mixture Model (GMM) and Support Vector Machine (SVM), along with i-vector algorithm. Performance of these two systems was evaluated using the same emotional speech database to identify four emotional speech signals: Angry, Happy, Sad and Neutral. Results were analyzed, and more than 75% of accuracy was obtained by both systems, which proved that our proposed i-vector algorithm can identify speech emotions with less error and with more accuracy.