Three-dimensional secondary global instability for the two-dimensional Stuart vortex of a free shear layer is investigated. That is in order to clarify an increase mechanism of the turbulence kinetic energy which is due to three-dimensional rib structure between rolls when the flow separation is achieved. We developed a program to compute the optimal transitional modes to amplify kinetic energy the most for the two-dimensional Stuart vortex base flow and compared the three-dimensional optimal growths for several Stuart vortex profiles, they correspond to which pulsation generates in downstream of a hump in DNS study. Results show that linear energy growth rate of turbulence component becomes large at the high-frequency case and small at the low-frequency case, that tendency does not correspond to which in DNS study. It implies that not only the linear growth but also nonlinear process should contribute to generate three-dimensional rib structure and increase turbulence energy.