A　provably　stable　summation-by-parts　simultaneous　approximation　term　(SBP-SAT)　finite-difference　time-domain　(FDTD)　subgridding　method　with　arbitrary　grid　ratios　is　pro-posed　to　accurately　and　flexibly　solve　2-D　electromagnetic　problems.　The　interpolation　matrix　with　the　grid　ratio　1:n　is　first　carefully　designed,　which　satisfies　the　norm-compatible　conditions　and　the　SBP　property　to　guarantee　long-term　stability.　By　introducing　a　virtual　intermediate　domain,　the　interpolation　matrix　with　an　arbitrary　grid　ratio　n:m　is　decomposed　into　two　interpolation　matrices　as　n:1　and　1:m.　By　combining　two　interpolation　matrices,　the　interpolation　matrix　with　an　arbi-trary　grid　ratio　is　derived,　which　is　flexible　to　model　complex　structures.　Five　numerical　examples　were　carried　out　to　validate　the　effectiveness　of　the　proposed　SBP-SAT　FDTD　subgridding　method　with　arbitrary　grid　ratios.　Results　show　that　it　can　flexibly　model　complex　structures　and　significantly　improve　computational　accuracy　and　efficiency.