The research on speech emotion recognition has become one of the interesting research themes in speech processing and in human-computer interaction (HCI) applications. In this paper, we present our work with the objective to recognize the Arabic user’s emotional state by analyzing the speech signal. We built an Arabic Emotional Speech corpus, covering five emotions - Happiness, Anger, Sadness, Surprise - and Neutrality. For classification, we adopted Supervised Learning approach, and implemented several classification algorithms: Support Vector Machines (SVM) with the Radial Basis Function (RBF) kernel, Neural Networks (NNs) and Deep learning approach using Recurrent Neural Network (RNNs). Since we consider emotion identification, we captured information related to the frequency and spectrum of the speech's signal. We calculated Mel-Frequency Cepstral Coefficients (MFCC) after applying High Pass Filter (HPF), and normalized the length of the features by using the (PCA) Principal Component Analysis. The comparison of the different classification methods on our Arabic Speech corpus showed that SVM approach performs better than the other two methods.