Channel　routing　is　a　key　problem　in　the　area　of　VLSI　layout.　Finding　a　minimum　width　solution　of　channel　routing　was　proved　to　be　NP-hard　by　Szymanski.　In　this　paper,　we　come　to　a　conclusion　that　the　minimum　parallel　clique　cover　of　$CCG$　is　equivalent　to　the　optimal　solution　of　2-layer　manhattan　channel　routing　where　vertical　constrains　are　noncyclic　and　extra　empty　columns　and　doglegs　are　not　allowed.　We　also　gave　a　new　heuristic　algorithm　based　on　the　conclusion　to　solve　the　problem　of　2-layer　manhattan　channel　routing.　©　2011　IEEE.