Global　routing　is　an　extremely　important　stage　of　very　large　scale　integration　(VLSI)　physical　design.　With　the　rise　of　nano-scale　integrated　circuit　design,　the　multilayer　global　routing　problem　has　attracted　considerable　research　interest　during　the　past　few　years.　In　this　article,　a　multilayer　X-architecture　global　routing　(ML-XGR)　system　based　on　particle　swarm　optimization　(PSO),　called　FZU-Router,　is　proposed　to　solve　the　ML-XGR　problem　for　the　first　time.　FZU-Router　contains　a　multilayer　X-architecture　integer　linear　programming　(MX-ILP)　model　and　a　multilayer　X-architecture　PSO　(MX-PSO)　algorithm,　which　are　presented　to　formulate　and　solve　the　ML-XGR　problem,　respectively.　Moreover,　four　effective　strategies　are　designed　to　enhance　the　efficiency　of　FZU-Router:　1)　a　strategy　for　generating　new　routing　modes　is　proposed　to　strengthen　the　robustness　of　encoding　strategy　of　MX-PSO;　2)　a　strategy　for　combining　MX-PSO　with　maze　routing　is　proposed　to　improve　the　routability;　3)　a　strategy　for　reducing　the　channel　capacity　is　proposed　to　make　better　use　of　optimization　ability　of　MX-PSO;　and　4)　a　strategy　for　dynamic　resource　assignment　is　proposed　to　make　better　use　of　routing　resources　and　shorten　the　running　time.　Experimental　results　on　multiple　benchmarks　confirm　that　the　proposed　FZU-Router　leads　to　fewer　total　overflow　and　shorter　total　wirelength　compared　with　the　state-of-the-art　routers.