The　mesh　network　is　a　new　emerging　wireless　technology　under　development　and　QoS　supporting　is　an　important　issue　in　it.　By　exploiting　the　advantages　of　multiple　radios　and　multiple　channels,　the　topology　of　a　wireless　mesh　network　is　in　fact　a　multi-graph　in　which　several　links　co-exists　among　two　neighbor　nodes.　In　this　work　we　study　the　problem　of　providing　bandwidth　guarantee　for　incoming　connection　request　in　the　mesh　network.　We　have　formally　described　a　new　path　bandwidth　calculation　solution　with　linear　programming　by　utilizing　the　multiple　links　among　the　neighbors.　Then　an　algorithm　based　on　the　breadth-first　search　is　developed　to　find　feasible　paths　with　end-to-end　bandwidth　guarantee.　And　a　heuristic　routing　scheme　is　also　proposed　to　find　the　path　in　a　distributed　manner.　Simulation　results　have　shown　that　the　proposed　solutions　have　good　performance　compared　with　the　related　works.　©　2012　Springer-Verlag　GmbH.