This paper describes a new formulation to solve the acoustic scattering problem by a non-convex structure. The presented hybrid algorithms connect the on-surface radiation condition method to accelerate the calculations with a two-dimensional finite element method to treat the non-convex part of the domain. This allows the problem of truncating the computational domain to be overcome. The variational formulations associated with a Dirichlet or a Neumann boundary condition are considered. Finally, we give some numerical results on a model test case to illustrate the improvement of accuracy of the new algorithm compared to a pure OSRC approach.