Multi-FPGA　prototype　design　is　widely　used　to　verify　modern　VLSI　circuits,　but　the　limited　number　of　connections　between　FPGAs　in　a　multi-FPGA　system　may　cause　routing　failure.　Therefore,　using　time-division　multiplexing　(TDM)　technology,　multiple　signals　are　transmitted　through　the　same　routing　channel　to　improve　utilization.　However,　the　performance　of　this　type　of　system　depends　on　the　routing　quality　within　the　FPGAs　due　to　the　signal　delay　between　FPGA　pairs.　In　this　paper,　we　propose　a　system-level　routing　method　based　on　TDM　to　minimize　the　maximum　TDM　ratio　that　satisfies　the　strict　ratio　constraint.　Firstly,　we　weight　the　edges　and　use　two　methods　to　build　approximate　minimum　Steiner　trees　(MST)　to　route　the　nets.　Then　we　propose　a　ratio　assignment　method　based　on　edge-demand　which　satisfy　the　TDM　ratio　constraint.　We　tested　our　method　with　the　benchmarks　provided　by　2019　CAD　Contest　at　ICCAD　and　compared　it　with　the　top　two.　The　experimental　results　shows　that　our　method　not　only　solves　all　problems　but　also　achieves　a　good　TDM　ratio.　©　2021,　Springer　Nature　Switzerland　AG.