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A new formulation of finite element-boundary integral (FE-BI) equations with non-overlapping and non-conforming domain decomposition method (DDM) is proposed to calculate electromagnetic scattering from cavities. The computational domain is divided into two parts: cavity and non-cavity domains. Tetrahedral elements with higher order and lower order vector basis functions are used in the cavity and non-cavity domains, respectively, and they are not conformal on the interface between two sub-domains. The application of Robin transmission condition at the aperture of the cavity relates the fields in the interior and exterior regions of the cavity. In addition, an effective preconditioner is designed to speed up the solution process of iterative solvers. Numerical results obtained show that the proposed method is suitable for this class of problems, and the preconditioner is highly effective to reduce the number of iterations for the solution.