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Base on the outer space search and the branch-and-bound framework, this paper presents an efficient outer space branch-and-bound algorithm for globally solving generalized linear multiplicative programming problem. First of all, we convert the problem into an equivalent problem. Then, by utilizing a direct relaxation method, we establish the linear relaxed problem to compute the lower bound of the global optimal value of the equivalent problem. By subsequently subdividing the initial outer space rectangle and solving a series of linear relaxed problems, the proposed algorithm is convergent to the global optimal solution of the primal problem. Finally, compared with some known algorithms, numerical experiments are given to demonstrate the feasibility and effectiveness of the proposed algorithm.