The　linear　canonical　transform(LCT)　is　a　parameterized　linear　integral　transform,　which　is　the　general　case　of　many　well-known　transforms　such　as　the　Fourier　transform(FT),　the　fractional　Fourier　transform(FRT)　and　the　Fresnel　transform(FST).　These　integral　transforms　are　of　great　importance　in　wave　propagation　problems　because　they　are　the　solutions　of　the　wave　equation　under　a　variety　of　circumstances.　In　optics,　the　LCT　can　be　used　to　model　paraxial　free　space　propagation　and　other　quadratic　phase　systems　such　as　lens　and　graded-index　media.　A　number　of　algorithms　have　been　presented　to　fast　compute　the　LCT.　When　they　are　used　to　compute　the　LCT,　the　sampling　period　in　the　transform　domain　is　dependent　on　that　in　the　signal　domain.　This　drawback　limits　their　applicability　in　some　cases　such　as　color　digital　holography.　In　this　paper,　a　Fast-Fourier-Transform-based　Direct　Integration　algorithm(FFT-DI)　for　the　LCT　is　presented.　The　FFT-DI　is　a　fast　computational　method　of　the　Direct　Integration(DI)　for　the　LCT.　It　removes　the　dependency　of　the　sampling　period　in　the　transform　domain　on　that　in　the　signal　domain.　Simulations　and　experimental　results　are　presented　to　validate　this　idea.