Computation　offloading　is　a　promising　way　to　improve　the　performance　as　well　as　reducing　the　battery　power　consumption　of　a　mobile　application　by　executing　some　parts　of　the　application　on　a　remote　server.　Recent　researches　on　mobile　cloud　computing　mainly　focus　on　the　code　partitioning　and　offloading　techniques,　assuming　that　mobile　codes　are　offloaded　to　a　prepared　server.　However,　the　context　of　a　mobile　device,　such　as　locations,　network　conditions　and　available　cloud　resources,　changes　continuously　as　it　moves　throughout　the　day.　And　applications　are　also　different　in　computation　complexity　and　coupling　degree.　So　it　needs　to　dynamically　select　the　appropriate　cloud　resources　and　offload　mobile　codes　to　them　on　demand,　in　order　to　offload　in　a　more　effective　way.　Supporting　such　capability　is　not　easy　for　application　developers　due　to　(　1)　adaptability:　mobile　applications　often　face　changes　of　runtime　environments　so　that　the　adaptation　on　offloading　is　needed.　(　2)　effectiveness:　when　the　context　of　the　mobile　device　changes,　it　needs　to　decide　which　cloud　resource　is　used　for　offloading,　and　the　reduced　execution　time　must　be　greater　than　the　network　delay　caused　by　offloading.　This　paper　proposes　a　framework,　which　supports　mobile　applications　with　the　context-aware　computation　offloading　capability.　First,　a　design　pattern　is　proposed　to　enable　an　application　to　be　computation　offloaded　on-demand.　Second,　an　estimation　model　is　presented　to　automatically　select　the　cloud　resource　for　offloading.　Third,　a　framework　at　both　client　and　server　sides　is　implemented　to　support　the　design　pattern　and　the　estimation　model.　A　thorough　evaluation　on　two　real-world　applications　is　proposed,　and　the　results　show　that　our　approach　can　help　reduce　execution　time　by　6-96%　and　power　consumption　by　60-96%　for　computation-intensive　applications.