Since the advent of the fast multipole method, large-scale electromagnetic scattering problems based on the electric field integral equation (EFIE) formulation are generally solved by a Krylov iterative solver. A well-known fact is that the dense complex non-hermitian linear system associated to the EFIE becomes ill-conditioned especially in the high-frequency regime. As a consequence, this slows down the convergence rate of Krylov subspace iterative solvers. In this work, a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary. Some numerical tests precise the behaviour of the new preconditioner. Moreover, comparisons are performed with the analytic preconditioner based on the Calderòn's relations for integral equations for several kinds of scatterers.