<p>The aim of this paper is to develop a novel global branch-reduction-bound algorithm for solving the sum of the general affine ratios programming (SGAR). Via exploiting equivalent conversion and linearization technique, the affine relaxation problem of the original problem is constructed. Next, according to the branch-and-bound framework, combined with acceleration technique, a unique global algorithm for the sake of the SGAR is proposed. It is demonstrated that the branch-reduction-bound algorithm finally converges to a global optimal solution of the SGAR. In the meantime, a thorough discussion of the computational complexity of the algorithm is performed. Finally, comparison of numerical experimental results indicate that the devised algorithm is robust.</p>