The paper deals with homologous topology optimization of structures undergoing large deformations. The objective function is defined so that the load-displacement curve follows the prescribed trajectry, which shows a typical snap-through buckling. The geometrically non-linear behavior of the structures is modeled using the total-Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. In order to escape from the singularity at critical points, the displacement control is utilized. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the sequential linear programming method. Two algorithms are proposed to obtain homologous deformation. Several numerical examples are demonstrated to validate the present optimization method.