Endmember extraction methods based on geometric?distribution of hyperspectral images usually divide into projection algorithm and the maximum volume formula for simplex, which the former has lower computational complexity and the latter has better precision. A Fast endmember extraction method based on Cofactor of a determinant Algorithm (FCA) is proposed. The algorithm combines the two kinds of algorithms, and which means it has a high speed and accuracy performance for endmember extraction. FCA finds the max volume of simplex by making pixels project to vectors, which are composed of the cofactors of elements in endmember determinant. Besides, FCA is flexible in endmember search, for it can use higher purity pixels to replace the endmembers extracted in the last iteration, which ensures that all the endmembers extracted by FCA are the vertices of simplex. The theoretical analysis and experiments on both simulated and real hyperspectral data demonstrate that the proposed algorithm is a fast and accurate algorithm for endmember extraction.