Microblogging　has　become　an　important　social　media　for　creating,　sharing,　or　exchanging　information　and　ideas.　Social　influence　analysis　in　Microblogging　is　often　exploited　for　different　tasks　such　as　information　retrieval,　recommendations,　businesses　intelligence.　Most　existing　methods　mostly　rely　on　social　links　between　users,　failing　to　take　advantage　of　characteristics　of　Microblogging.　Furthermore,　the　size　of　Microblogging＇s　user　(i.e.　Microblogger)　is　very　large,　which　makes　computing　resource　for　social　influence　mining　approach　can＇t　be　satisfied　by　single　computer.　In　this　paper,　a　tensor　factorization　framework　based　on　cloud　computing　platform　is　proposed　for　mining　social　influence　in　Microblogging.　The　framework　has　three　components:　a　feature　extraction　component,　a　tensor　factorization　component　and　a　user　influence　ranking　component.　In　feature　extraction　component,　features　are　extracted　for　capturing　user　social　influence　quantitatively　through　statistical　analysis　on　the　Microbloggers＇　relations.　In　tensor　factorization　component,　tensor　factorization　based　MapReduce　model　is　presented　to　infer　user＇s　implicit　user＇s　relations.　Finally,　a　user　influence　ranking　function　is　constructed　for　computing　user　social　influence　in　user　influence　ranking　component.　Experiments　on　Sina　weibo　dataset　(Chinese　Microblogging　platform)　show　that　our　proposal　significantly　not　only　improves　the　prediction　accuracy　compared　with　two　baseline　methods,　but　also　has　competitive　advantage　for　processing　massive　data　from　Microblogging