In this paper, we want to solve the singular semi-Sylvester equation using the Drazin-inverse and the Drazin-inverse generalized minimum residual method (DGMRES(m) algorithm). First, we transform the semi-Sylvester equation into a multiple linear systems. Then, we present the conditions and assumptions needed to apply the DGMRES(m) algorithm. We compare our proposed method with the Galerkin projection method in point of view CPU-time, accuracy and iteration number. Finally, by some numerical experiments, we show the efficiency of the proposed method.