This　brief　focuses　on　solving　the　tracking　problem　of　swarm　robots　with　a　non-cooperative　target,　where　two　core　issues　namely　non-cooperative　target　and　cross-domain　collaboration　are　both　taken　into　account.　In　order　to　solve　the　former　issue,　the　trajectory　of　the　non-cooperative　target　is　constructed　by　a　network　model.　This　is　more　superior　than　the　target　system　matrix　observer-based　method　that　adopted　extensively　in　literature,　as　the　latter　one　will　cause　the　self-loop　problem.　Besides,　the　target　information　is　no　longer　required　in　solving　the　regulation　equation.　Furthermore,　a　fixed-time　cross-domain　control　method　merely　relying　on　outputs　of　a　robot　and　its　neighbours　is　proposed.　Namely,　the　network-based　fixed-time　control　method　proposed　in　this　brief　is　fully　distributed　without　self-loop　and　requirement　of　the　non-cooperative　target＇s　system　matrix.　With　the　proposed　controller,　the　cross-domain　robots　are　able　to　successfully　track　a　non-cooperative　target　within　a　fixed　time,　which　is　also　verified　by　some　numerical　simulations.