Abstract: Frequency-modulated continuous-wave (FMCW) radar，as a kind of radar systems with lightweight, low cost and high resolution, has attracted widespread attention and already reflected tremendous applicable value both in military and civil use. However, the nonlinearity introduced by modulation is a bottleneck to the utilization of FMCW radars. Typical nonlinearity correction method can estimate the nonlinearity to a certain degree, whereas the problem of error propagation in the estimation processing leads to a defective nonlinearity correction. Focusing on this problem, a novel algorithm based on polynomial regression is proposed in this paper to estimate the nonlinearity accurately. The proposed algorithm models the nonlinearity phase as a polynomial function and estimates the corresponding coefficients jointly through the polynomial regression algorithm (PRA), so that the error propagation is avoided. Based on the coefficients estimated, the nonlinearity correction is implemented with the help of time resampling procedure. Simulation results of the proposed algorithm indicate that not only the nonlinearity can be estimated accurately, but also the estimation performance is closer to the Cramer-Rao lower bound (CRLB) in high signal to noise ratio (SNR), compared with the conventional method. Real data processing result of an X-band FMCW radar indicates that the nonlinearity can be eliminated effectively with the proposed algorithm.