A differential FMCW LiDAR for high-precision distance measurements of remote non-stationary targets is proposed and demonstrated experimentally. The required positive and negative symmetrically oppositely chirped laser beams are generated synchronously through a fixed-frequency laser by employing externally unified broadband optical phase modulation and symmetrical dual-sideband optical filtering. After coaxial transmission and reception, orthogonally polarized optical beat signals containing target distance and vector velocity data are de-chirped separately by optical in-phase and quadrature demodulations and then synchronously received by four-channel photoelectric balance detectors. After differential processing of the received beat signals and a fast Fourier transform, it is possible to implement real-time simultaneous range and vector velocity measurements. The inherent symmetrically oppositely chirped optical frequency make it possible to measure the target distance immune to the internal random phase noise introduced by the spectral linewidth of the frequency-swept laser and the external random phase noise introduced by atmospheric turbulence, speckle, and vibration. Meanwhile, the measurement of the target velocity is immune to the nonlinearity of the frequency-swept laser. These results encourage an approach to overcome the barriers of coherence length, nonlinearity, and external noise, and implement simultaneous real-time ranging and velocimetry of long-range, rapid-moving targets.