This　article　presents　a　method　to　achieve　a　high　precision　time-frequency　analysis　and　detect　the　linearity　of　linear　frequency　modulation　continuous　wave　(LFMCW)　radar　system.　At　first,　discrete　time　domain　window　is　used　to　make　the　target　signal　to　be　discrete　short-time　pieces.　The　fractional　Fourier　transform　(FRFT)　is　used　to　calculate　the　frequency　modulation　(FM)　rates　of　every　subsection.　Let　the　short-time　signal　mix　with　a　ideal　linear　frequency　modulation　(LFM)　signal,　the　intermediate　frequency　(IF)　signal　can　be　obtained.　The　Wigner-Ville　Distribution　(WVD)　transform　can　be　used　to　estimate　the　time-frequency　function　of　the　IF　signal.　The　time-frequency　function　of　short-time　signal　can　be　calculated　from　the　relation　between　the　IF　signal　and　the　ideal　LFM　signal.　This　method　can　achieve　a　high　precision　time-frequency　analysis.　The　simulation　can　show　a　significant　resolution　performance　improvement　over　the　conventional　method.　At　last,　a　practical　engineering　application　measurement　is　presented.　©　2017,　North　Atlantic　University　Union.　All　rights　reserved.