The presence of range and azimuth (or Doppler) ambiguities in synthetic aperture radars (SARs) is well known. The ambiguity noise is related to the antenna pattern and the value of pulse repetition frequency (PRF). Because a new frequency modulated continuous wave (FMCW) SAR has the characters of low cost and small size, and the capacity of real-time signal processing, the antenna will likely vibrate or deform due to a lack of the stabilized platform. And the value of PRF cannot be much high because of the high computation burden for the real-time processing. The aim of this study is to access and improve the performance of a new FMCW SAR system based on the ambiguity noise. First, the quantitative analysis of the system's ambiguity noise level is performed; an antenna with low sidelobes is designed. The conclusion is that the range ambiguity noise is small; the azimuth ambiguity noise is somewhat increased, however, it is sufficiently small to have marginal influence on the image quality. Finally, the ambiguity noise level is measured using the imaging data from a Ku-band FMCW SAR. The results of this study show that the measured noise level coincides with the theoretical noise level.