Nowadays,　Fast　Fourier　Transform　(FFT)　is　applied　in　various　industries,　which　facilitates　the　development　of　human　society.　Besides,　this　algorithm　is　improving　continuously　in　the　meantime.　This　paper　is　to　introduce　the　historical　background,　mathematical　theory　and　several　applications　of　Fast　Fourier　Transform　(FFT),　and　to　explore　a　method　for　solving　linear　two-point　boundary　value　problem　using　this　algorithm　in　details.　Finally,　based　on　the　above,　the　analysis　and　discussion　of　the　results　is　shown.　©　2021　IEEE.