We propose an algorithm for facial expression recognition which can classify the given image into one of the seven basic facial expression categories (happiness, sadness, fear, surprise, anger, disgust and neutral). PCA is used for dimensionality reduction in input data while retaining those characteristics of the data set that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Such low-order components contain the "most important" aspects of the data. The extracted feature vectors in the reduced space are used to train the supervised Neural Network classifier. This approach results extremely powerful because it does not require the detection of any reference point or node grid. The proposed method is fast and can be used for real-time applications.