The inverse scattering problem for coupled wave equations has various applications such as waveguide filter design and electric transmission line fault diagnosis. In this paper, an efficient numerical algorithm is presented for solving the inverse scattering problem related to generalized Zakharov-Shabat equations with two potential functions. Inspired by the work of Xiao and Yashiro on Zakharov-Shabat equations with a single potential function, this new algorithm considerably improves the numerical efficiency of an algorithm proposed by Frangos and Jaggard, by transforming the original iterative algorithm to a one-shot algorithm.