Electromagnetic scattering by perfect electrically conducting (PEC) objects in a layered medium is studied in this paper. The layered medium Green's function is adopted as the kernel of the electric field integral equation (EFIE) so that the effects from the multilayered background can be accounted for automatically. However, the spectrum of the EFIE with this kernel, is unfortunately undesirable. This leads to slow convergence of the iterative solution. To improve the convergence, the Calderón identities are derived and leveraged to precondition the EFIE. By utilizing Buffa-Christiansen (BC) basis function in discretizing the preconditioning operator, the preconditioner can be made completely multiplicative. Different numerical examples are designed to show the performance of the preconditioner. It is shown that the proposed preconditioner makes the EFIE system with layered kernel converge rapidly, independent of the discretization density.