In order to address the problem of surveillance for anti-UAV, frequency-modulated continuous wave (FMCW) radar is commonly used to detect the slow-moving target such as the UAVs, due to its capability of high-precision measurement and non-blind zone in close range. In order to improve the detection efficiency, a new kind of adaptive clutter suppression filter is proposed for FMCW radar. The filter is able to suppress the strong ground cutter and improve the performance. Results from a FMCW radar which has a linear frequency modulation (LFM) waveforms whose bandwidth is 150MHz show that under the effects of the background strong clutter, the signal-to-noise ratio of the analysis results after the adaptive filter processing is improved by 12dB. The proposed filter shows better performance in terms of suppressing background clutter and extracting moving target compared to the moving target indication (MTI) pulse cancellation filter.