This paper proposes a low complexity super resolution algorithm for frequency modulated continuous wave (FMCW) radar systems for foreign object debris (FOD) detection. FOD radar has a requirement to detect foreign object in small units in a large area. However, The fast Fourier transform (FFT) method, which is most widely used in FMCW radar, has a disadvantage in that it can not distinguish between adjacent targets. Super resolution algorithms have a significantly higher resolution compared with the detection algorithm based on FFT. However, in the case of the large number of samples, the computational complexity of the super resolution algorithms is drastically high and thus super resolution algorithms are difficult to apply to real time systems. In order to overcome this disadvantage of super resolution algorithm, first, the proposed algorithm coarsely obtains the frequency of the beat signal by employing FFT. Instead of using all the samples of the beat signal, the number of samples is adjusted according to the frequency of the beat signal. By doing so, the proposed algorithm significantly reduces the computational complexity of multiple signal classifier (MUSIC) algorithm. Simulation results show that the proposed method achieves accurate location even though it has considerably lower complexity than the conventional super resolution algorithms.