This　article　presents　a　discrete　mathematical　model　for　fan　blades　and　theoretically　analyses　the　mathematical　relationship　between　the　location　and　depth　of　crack　and　fan　blade　natural　frequency.　On　the　basis　of　the　blade　mathematical　model,　using　the　theoretical　computed　natural　frequency　as　the　fault　feature,　this　article　proposes　a　fast　and　efficient　fan　blade　crack　fault　diagnosis　method.　Transfer　matrix　method　is　used　to　calculate　the　first　three-order　blade　natural　frequencies　under　different　crack　cases　and　then　to　build　the　database　in　MATLAB.　Subsequently,　the　damaged　blade　can　be　detected　using　changes　in　natural　frequencies　by　solving　the　reverse　problem.　The　experimental　result　shows　that　this　discrete　mathematical　model　can　get　the　exact　solution　of　natural　frequency,　and　the　method　has　certain　application　value.