In　this　article,　to　improve　the　achievable　sum-rate　of　the　multi-user　millimeter　wave　(mmWave)　communication　in　densely　blocked　areas,　we　design　a　multi-route　multi-hop　(MRMH)　cascaded　intelligent　reflecting　surface　(IRS)-aided　system.　In　our　designed　system,　we　aim　to　maximize　the　achievable　sum-rate　for　the　multiple　users　by　jointly　optimizing　the　phase　shifts　(PSs)　at　the　multiple　IRSs　and　the　active　beamforming　vector　(ABV)　at　the　base　station　(BS).　To　achieve　this　target,　we　formulate　an　optimization　problem.　However,　it　is　non-convex　and　difficult　to　be　solved.　By　considering　the　sparse　scattering　and　near-orthogonality　characteristics　of　the　mmWave　channels,　we　divide　the　optimization　problem　into　multiple　tractable　sub-problems　and　obtain　a　near-optimal　solution.　The　simulation　results　prove　that　the　proposed　scheme　has　better　performance　than　the　existing　schemes.　Furthermore,　we　prove　the　effectiveness　of　the　multi-hop　IRS-aided　system　by　comparing　the　single-hop　IRS-aided　system.　©　1967-2012　IEEE.