Linear Frequency Modulation (LFM) is widely used in radar and sonar scenarios. However, the Doppler tolerance of LFM signal is not ideal. When the unidirectionally modulated LFM signal is in distance measurement, the Doppler delay of the matched filter output cannot be eliminated, and thus there is a ranging error. After the positive and negative Frequency Modulation (FM) echo signals, which is based on the same frequency band, are matched and filtered, the delay caused by Doppler is the same and the direction is opposite. By using the inverse time delay difference of the positive and negative FM, speed can be measured, and the ranging error in the ranging of unidirectionally modulated LFM signal can also be eliminated. In this paper, based on the analysis of the influence of target moving speed on LFM signal ranging, a positive and negative Linear frequency modulation method for Ranging and Speed measurement (LRS) is proposed. Extensive simulation results show that the proposed LRS method can better estimate the distance and speed of moving targets, and it has reference value for engineering application.