Graph　routing　problem　(GRP)　and　its　generalizations　have　been　extensively　studied　because　of　their　broad　applications　in　the　real　world.　In　this　paper,　we　study　a　variant　of　GRP　called　the　general　cluster　routing　problem　(GCRP).　Let　G=(V,E)　be　a　complete　undirected　graph　with　edge　weight　c(e)　satisfying　the　triangle　inequality.　The　vertex　set　is　partitioned　into　a　family　of　clusters　C1,..,　Cm.　We　are　given　a　required　vertex　subset　V¯　⊆　V　and　a　required　edge　subset　E¯　⊆　E.　The　aim　is　to　compute　a　minimum　cost　tour　that　visits　each　vertex　in　V¯　exactly　once　and　traverses　each　edge　in　E¯　at　least　once,　while　the　vertices　and　edges　of　each　cluster　are　visited　consecutively.　When　the　starting　and　ending　vertices　of　each　cluster　are　specified,　we　devise　an　approximation　algorithm　via　incorporating　Christofides’　algorithm　with　minimum　weight　bipartite　matching,　achieving　an　approximation　ratio　that　equals　the　best　approximation　ratio　of　path　TSP.　Then　for　the　case　there　are　no　specified　starting　and　ending　vertices　for　each　cluster,　we　propose　a　more　complicated　algorithm　with　a　compromised　ratio　of　2.67　by　employing　directed　spanning　tree　against　the　designated　auxiliary　graph.　Both　approximation　ratios　improve　the　state-of-art　approximation　ratio　that　are　respectively　2.4　and　3.25.　©　2021,　Springer　Nature　Switzerland　AG.