The dimension reduction is of significance to the interpretation of hyperspectral images. The classical Principal Component Analysis (PCA) method based on Second-order Statistics (SOS) may lose the signals of small targets during dimension reduction. To solve this problem, the PCA method is extended by using high-order statistics as projection indexes and a hyperspectral image dimension reduction method based on multi-index successive projection is proposed. The method incorporates the features of the non-orthogonal projection while retaining the advantages of the PCA method. It can keep the abnormal signal components in the dimension-reduced space. The experimental result of the real hyperspectral image data shows that this method can extract more complete signal subspace than the PCA method.