Convolutional　neural　network　(CNN)-based　single　image　super-resolution　(SR)　methods　have　achieved　superior　performance　on　some　discrete-scaling　factors,　including　2,　3,　and　4.　However,　the　scaling　factors　for　SR　should　be　continuous　and　not　discrete　in　practical　applications.　Previous　CNN-based　SR　models　usually　yield　poor　results　for　non-integer-scaling　factors　and　are　sometimes　even　worse　than　results　derived　from　the　conventional　bicubic　method.　To　extend　CNN-based　SR　models　to　continuous　scale,　this　paper　proposes　a　multiple-scaling-based　SR　(MSSR)　method　that　combines　an　integer-scaling-factor　SR　and　once　or　twice　non-integer-scaling-factor　SR　without　retraining　networks.　For　a　non-integer-scaling　factor,　the　MSSR　method　first　computes　an　optimal　integer-scaling　factor　according　to　the　data　similarity　and　choose　the　corresponding　pre-trained　model　for　the　next　stage.　Then,　an　existing　CNN-based　model　is　used　to　perform　the　integer-scaling-factor　SR.　Finally,　the　output　is　scaled　to　the　target　size.　The　proposed　MSSR　method　can　extend　a　variety　of　existing　CNN-based　SR　models　from　discrete　to　continuous-scaling　factors.　Experimental　results　with　six　CNN-based　SR　models　demonstrated　that　the　MSSR　method　could　effectively　improve　the　performance　of　existing　CNN-based　SR　models　for　continuous-scaling-factor　SR　without　retraining　networks.　Furthermore,　the　comparison　with　a　magnification-arbitrary　method,　called　Meta-SR,　shows　that　the　proposed　MSSR　method　usually　outperforms　Meta-SR　for　scaling　factors　greater　than　or　equal　to　2.