A new type of matrices which is called as the first and the last difference r-circulant matrix (FLDcirc_r matrix) was presented.The linear operation, the matrix product, the inverse matrix of this type of matrices were verified to be still FLDcirc_r matrices.Through constructing the basic FLDcirc_r matrix, the discriminance for FLDcirc_r matrices and the fast algorithm for their inverse and generalized inverse were provided.