Abstract: A hybrid algorithm based on Direct Inversion in Iterative Subspace (DIIS) algorithm is developed for rapid solution of atomic and molecular Hartree-Fock equations. The improved algorithm uses mixing of subspaces with different sizes to increase the weight of Fock matrix closer to convergence, and the mixed Fock matrix is used as a starting point of new iteration. This algorithm reduces effectively the number of iterations in SCF process. Compared with DIIS algorithm before mixing, it is found that this algorithm is superior to the DIIS algorithm with two different subspaces, and the computational cost is effectively reduced.