Abstract: The combination of frequency-modulated continuous-wave (FMCW) technology and synthetic aperture radar (SAR) techniques have a lot of advantages, such as light weight, low probability of intercept and high resolution imaging. One limiting factor to the use of FMCW sensors is the presence of nonlinearities in the transmitted signal. In order to analyze the problem of large nonlinear error in frequency modulated continuous wave imaging system with X-band and 4.8GHz bandwidth, a nonlinear correction algorithm based on high order ambiguity function and resampling is proposed. Polynomial-phase signals are fitted by the nonlinear beat-frequency signals combing with frequency-voltage character of voltage controlled oscillator in this paper. Polynomial-phase coefficients are estimated by HAF, and then nonlinear error is corrected by interpolation method. The experimental results based on simulation and real data indicate that this method can correct the nonlinear error with high precision and strong engineering applicability can solidly and effectively corrects the nonlinear error in FMCW system.