In this paper, we propose to combine the twodimensional MUSIC (MUltiple SIgnal Classification) algorithm with Fast Fourier Transform (FFT) to detect small moving targets from raw data collected by millimeter-wave beamscanners. It is shown that this hybrid detection method makes it possible to reduce by factor 3 the computation time required by MUSIC algorithm, at the expense of the reduction by 55% of the detection rate. Measurement results and analyses are given in the case of the tracking of a small mobile cylinder in a cluttered indoor environment from three millimeter-wave beamscanning radars.