One of the main reasons for serious road accidents is driving while drowsy. For this reason, drowsiness detection and warning system for drivers has recently become a very important issue. Monitoring physiological signals provides the possibility of detecting features of drowsiness and fatigue of drivers. One of the effective signals is to measure electroencephalogram (EEG) signals and electrooculogram (EOG) signals. The aim of this study is to extract drowsiness-related features from a set of EEG signals and to classify the features into three states: alertness, drowsiness, sleepiness. This paper proposes a drowsiness detection system using Linear Predictive Coding (LPC) coefficients and Support Vector Machine (SVM). Samples of EEG data from each predefined state were used to train the SVM program by using the proposed feature extraction algorithms. The trained SVM program was tested on unclassified EEG data and subsequently reviewed according to manual classification. The classification rate of the proposed system is over 96.5% for only very small number of samples (250ms, 64 samples). Therefore, it can be applied to real driving incident situation that can occur for a split second.