The general field of the invention is that of Doppler lidars intended to measure the speed of a target. The lidar according to the invention comprises:First means for modulating the optical frequency of the transmission signal, said frequency being the sum of a constant frequency and of a variable frequency of determined amplitude modulated by a periodic temporal function;Second means for computing the spectrum of the measured heterodyne signal and for creating two measurement spectra obtained by shifting the spectrum of the heterodyne signal by a positive and negative frequency value, said realignment frequency equal to the difference between the instantaneous frequency of the transmission signal and the frequency of a signal transmitted at a time shifted by the round-trip travel time between the lidar and the target;Third means for comparing the two measurement spectra, the difference in amplitude between the two spectra at the Doppler frequency determining the direction of the speed of the target.