In this paper, constant false alarm rate (CFAR) detector-based approaches are proposed for interference mitigation of Frequency modulated continuous wave (FMCW) radars. The proposed methods exploit the fact that after dechirping and low-pass filtering operations the targets’ beat signals of FMCW radars are composed of exponential sinusoidal components while interferences exhibit short chirp waves within a sweep. The spectra of interferences in the time-frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> ) domain are detected by employing a 1-D CFAR detector along each frequency bin and then the detected map is dilated as a mask for interference suppression. The proposed approaches are applicable to the scenarios in the presence of multiple interferences. Compared to the existing methods, the proposed methods reduce the power loss of useful signals and are very computationally efficient. Their interference mitigation performances are demonstrated through both numerical simulations and experimental results.