This paper presents the mode matching (MM)/finite element method (FEM) hybrid analysis for a short-slot 2-plane coupler, and an optimization process for a wideband design based on a genetic algorithm (GA). The method of the analysis combines a fast modal analysis of the MM which reduces the computation time, with the flexibility of an FEM which can be used with an arbitrary cross-section. In the analysis, the model is reduced into the one-eighth model by using the three-dimensional structural symmetry. The computed results agree well with those by the simulation and the computation time is reduced. The bandwidth is improved by the optimization based on the GA from 2.4% to 6.9% for the 2-plane hybrid coupler and from 5.4% to 7.5% for the 2-plane cross coupler. The measured results confirm the wideband design.