<p>The research goal of this paper is to design a global optimization algorithm (GOA) for solving the minimax affine fractional programming problem (MAFP) globally, which benefits from a novel relaxation optimization plan and branch-and-bound framework in the reduced space. For this research goal, problem (MAFP) is first formulated to an equivalent lifted problem (ELP) by introducing some auxiliary variables to do equivalent conversion. For the form of problem (ELP), an initial rectangle and a latest equivalence problem (EP) are constructed by adding some new variables. Secondly, a novel relaxation optimization plan is formulated to get a linear optimization problem (LOP) of problem (EP). Next, the detailed procedures of the algorithm (GOA) are given. Furthermore, theoretical analysis of the algorithm (GOA) is presented from the perspectives of convergence and complexity. Finally, to verify the validity and robustness of the algorithm (GOA), the algorithm (GOA) is used to solve some test cases, the numerical experiment results are very exciting.</p>