Ant　colony　optimization　(ACO)　is　a　population-based　metaheuristic　technique　to　effectively　solve　combination　optimization　problems.　However,　it　is　still　an　active　research　topic　how　to　improve　the　performance　of　ACO　algorithms.　Though　there　are　many　algorithms　to　effectively　solve　traveling　salesman　problems　(TSPs),　there　is　an　application　bottleneck　that　the　ACO　algorithm　costs　too　much　time　in　order　to　get　an　optimal　solution.　To　improve　the　time　performance　of　ACO　in　solving　large　scale　TSPs,　a　fast　algorithm　is　presented　in　this　paper.　Firstly,　a　novel　multiple-grain　representation　model　of　TSPs　is　proposed.　Based　on　the　model,　a　new　algorithm　for　TSPs　is　presented,　which　mainly　contains　six　phases,　i.e.　a　granularity　partition　algorithm　based　on　density　clustering,　an　ACO　algorithm　based　on　the　coarse　grain,　a　connection　algorithm　between　two　granularities,　an　ACO　algorithm　in　the　same　granularity,　a　fusion　algorithm　among　granularities,　and　a　subsection　optimization　algorithm　regardless　of　granularities.　The　analysis　of　computation　complexity　and　the　experimental　results　for　large　number　of　TSPs　demonstrate　that　the　proposed　algorithm　can　greatly　improve　the　speed　of　convergence　in　contrast　to　the　classical　ACO　algorithm,　and　is　highly　competitive　in　time　performance　compared　with　some　latest　elitist　ACO　algorithms.