Strain　is　a　useful　method　to　manipulate　properties　of　three-dimensional　(3D)　topological　insulators　(TIs).　In　this　study,　we　demonstrate　the　possibility　to　tune　the　circular　photogalvanic　effect　(CPGE)　of　surface　states　of　3D　TI　Sb2Te3　films　by　applying　external　strain.　The　CPGE　of　3D　TI　Sb2Te3　grown　on　SrTiO3　(STO)　with　different　thicknesses　has　been　systematically　investigated.　It　is　found　that　as　the　thickness　of　Sb2Te3　films　increases　from　7-quintuple　layer　(QL)　to　27-QL,　the　CPGE　current　first　increases　and　then　decreases.　Additionally,　the　CPGE　currents　demonstrate　remarkable　temperature　dependence,　which　even　reverse　sign　when　the　temperature　is　increased　from　77　to　300　K.　This　phenomenon　is　due　to　the　vertical　thermoelectric　effect　and　inverse　spin　Hall　effect.　Finally,　the　CPGE　measurements　of　Sb2Te3　films　under　different　mechanical　strains　are　performed,　and　it　is　found　that　the　CPGE　current　linearly　decreases　with　the　increase　in　the　external　strain.　The　variation　in　the　CPGE　current　can　be　tuned　up　to　11%　and　44%　in　the　18-　and　12-QL　Sb2Te3　grown　on　STO　substrates　under　a　tensile　strain　of　0.0225　and　0.0066,　respectively.　In　particular,　it　can　even　reach　100%　in　the　30-QL　Sb2Te3　film　grown　on　an　InP　substrate　under　a　tensile　strain　of　0.0033,　which　is　due　to　the　combined　effect　of　mechanical　deformation　and　spin　injection　from　substrates.　Our　work　provides　a　method　to　effectively　manipulate　the　CPGE　in　3D　TIs　by　the　combined　effect　of　mechanical　strain　and　spin　injection　from　substrates,　which　paves　the　way　for　novel　opto-spintronic　devices.