One-bit radar involving direct one-bit sampling is a promising technology for many civilian applications due to its low-cost and low-power consumptions. In this paper, problems encountered by one-bit LFMCW radar are studied and a two-stage target detection approach termed as DR-GAMP is proposed.Firstly, the spectrum of one-bit signal in a scenario of multiple targets is analyzed. It is indicated that high-order harmonics may result in false alarms (FAs) and cannot be neglected. Secondly, DR-GAMP is used to suppress the high order harmonics. Specifically, linear preprocessing and predetection are proposed to perform dimension reduction (DR), and then, generalized approximate message passing (GAMP) is utilized to suppress high-order harmonics. Finally, numerical simulations are conducted to evaluate the performance of one-bit LFMCW radar with typical parameters. It is shown that compared to conventional radar with linear processing approach, one-bit LFMCW radar has 0.5 dB performance gain when the input signal-to-noise ratios (SNRs) of targets are low. Moreover, it has 1.6 dB performance loss in a scenario with an additional high SNR target.