Recently, computing the capacity region of the degraded broadcast channel (DBC) was showed as a nonconvex optimization problem by Calvo et al . There seems to be no efficient method to solve in polynomial time due to the lack of convexity. In other nonconvex optimization problem, however, Kumar et al showed that Arimoto-Blahut type algorithm converges to the global optimum when some conditions hold . In this paper, we present Arimoto-Blahut type algorithm toward computing the capacity region of the DBC. By using Kumar's method, we prove the global convergence of the algorithm when some conditions hold and derive an expression for its convergence rate.