Linearity of VCO directly impacts on the range resolution of LFMCW radar, therefor, a linearity correction based on linearity detection is usually adoptted in practical applications. This paper proposes a new method of rapid linearity detection of LFMCW radar. First, estimate and correct the instantaneous phase. Then, fit a straight line for the instantaneous phase of difference frequency signal by least square approximation algorith. Finally, estimate the instantaneous Frequency-Modulation rate of FM signal. Simulation results show that the method is valid.