These Electroencephalography (EEG) signals is an effective tool for identification, monitoring, and treatment of epilepsy, but EEG signals need highly experienced personnel to interpret it correctly due to its complexity, even for an expert it is monotonous and usually consume much time. Therefore, the automatic computer-aided device (CAD) needs to be developed to overcome those challenges associated with epilepsy interpretation and diagnosis. The system efficiency relies largely on the quality of features supply as input to classifiers. This paper presents an efficient feature extraction technique to develop a CAD system that can detect and classify normal, interictal and ictal epilepsy signals correctly with high accuracy. Our approach employs time-frequency features, statistical features and nonlinear features combined as hybrid features to train and test the classifier. Machine learning classifiers of multi-class support vector machine (mSVM) and feed-forward neural network (FFNN) with fivefold cross-validation are used to classifies normal, interictal and ictal with our proposed features. Our system was tested using a publicly available database with three classes each of 100 single channels EEG signals of 4096 samples point each. Based on sensitivity, specificity, and accuracy, our proposed approach of multiclass classification shows a good performance with 96.7%, 98.3% and 100% of sensitivity, specificity, and accuracy respectively.