The resolution of LFMCW (Linear Frequency Modulation Continuous Wave) range radar is remarkably high. However, blind zone and nonlinearity reduce its performance. In this article, a novel hardware design to improve the blind zone is presented. The nonlinearity is analyzed, and a novel method is used to correct the nonlinearity and the proposed method also has a beneficial effect on white noise. Based on the proposed method, the Monte-Carlo simulations are presented and a short-range measurement system at 24 GHz is fabricated and evaluated. The experimental results show that the blind zone is about 30 cm and the ranging error is less than 10 mm in 15 m.