In this article, we present some formulas of the Drazin inverses of the sum of two matrices under the conditions P2QP = 0; P2Q2 = 0, QPQ = 0 and PQP2 = 0; PQ2 = 0, QP3 = 0 respectively. These conditions are weaker than those used in some literature on this subject. Furthermore, we apply our results to give the representations for the Drazin inverses of block matrix A B C D (A and D are square matrices) with generalized Schur complement is zero.
