<p>This paper presents a novel branch-and-bound algorithm for globally solving generalized linear fractional-multiplicative programming (GLFMP) problems. In this algorithm, the intricate GLFMP problem is first transformed into a nonlinear programming problem with nonlinear constraints by applying intermediate variables. Subsequently, to tackle its nonlinear facet, a new linear relaxation problem was constructed by applying the linear relaxation strategy. Furthermore, the algorithm’s termination speed is enhanced by introducing region reduction techniques and an adaptive branching rules into its output space. By establishing the algorithm’s global convergence and analyzing its computational complexity, we estimate the maximum total number of iterations. Ultimately, the numerical results demonstrate that the algorithm can effectively solve the GLFMP problem within a specific case.</p>