This paper presented an efficient algorithm for addressing large-scale linear fractional program problems, which are widely used in hospital management. First of all, we converted the initial problem into an equivalent problem by applying the Charnes-Cooper transformation technique. Next, by directly relaxing the nonlinear constraints, a mixed-integer linear relaxation problem was then constructed. Subsequently, by successively partitioning the initial output space rectangle and solving a series of mixed-integer linear relaxation problems, we proposed an efficient branch-relaxation-bound algorithm for globally addressing large-scale linear fractional program problems for the first time. Moreover, the computation complexity of the algorithm was analyzed, and the maximum number of iterations of the algorithm in the worst-case scenario was estimated. Furthermore, the experimental results demonstrated the high efficiency of the proposed algorithm in solving the investigated large-scale linear fractional program problem.