In this paper, we propose a fast algorithm for principal component analysis (PCA) dealing with large high-dimensional data sets. A large data set is firstly divided into several small data sets. Then, the traditional PCA method is applied on each small data set and several eigenspace models are obtained, where each eigenspace model is computed from a small data set. At last, these eigenspace models are merged into one eigenspace model which contains the PCA result of the original data set. Experiments on the FERET data set show that this algorithm is much faster than the traditional PCA method, while the principal components and the reconstruction errors are almost the same as that given by the traditional method.