Face recognition is one of the most important image processing research topics which is widely used in personal identification, verification and security applications. In this paper, a face recognition system, based on the principal component analysis (PCA) and the feedforward neural network is developed. The system consists of two phases which are the PCA preprocessing phase, and the neural network classification phase. PCA is applied to calculate the feature projection vector of a given face which is then used for face identification by the feedforward neural network. The proposed PCA and neural network based identification system provides improvement on the recognition rates, when compared with a face classifier based on the PCA and Euclidean Distance.