A　hybrid　surface　integral　equation　partial　differential　equation　(SIE-PDE)　formulation　with　non-conformal　meshes　is　proposed　to　solve　the　electromagnetic　problems.　An　equivalent　model　with　only　the　electric　current　density　is　first　constructed　for　piecewise　homogeneous　media,　which　is　then　enforced　into　the　Helmholtz　equation　as　an　excitation.　A　connection　matrix　is　carefully　constructed　to　couple　the　SIE　and　PDE　formulations　without　any　additional　requirements　upon　the　boundary　conditions　and　meshes.　Therefore,　non-conformal　meshes　are　fully　supported,　which　is　extremely　flexible　to　model　complex　structures.　Numerical　results　show　that　it　is　accurate,　efficient　and　flexible　to　solve　electromagnetic　problems.　©　2022　IEEE.