Theregularizedimageinterpolationmethodiswidelyusedbasedonthevectorinterpolationmodelinwhichdown-samplingmatrixhasverylargedimensionandneedslargestorageconsumptionandhighercomputationcomplexity.Inthispaper,afastalgorithmforimageinterpolationbasedonthetensorproductofmatricesispresented,whichtransformsthevectorinterpolationmodeltomatrixform.Theproposedalgorithmcanextremelyreducethestoragerequirementandtimeconsumption.Thesimulationresultsverifytheirvalidity.