In this paper, we give the results for the Drazin inverse of P + Q, then derive a representation for the Drazin inverse of a block matrix $M = \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ under some conditions. Moreover, some alternative representations for the Drazin inverse of $M^D$ where the generalized Schur complement $S = D - CA^DB$ is nonsingular. Finally, the numerical example is given to illustrate our results.