We propose a novel, to the best of our knowledge, distance recovery method via swept frequency mixing for frequency-modulated continuous wave (FMCW) light detection and ranging (LiDAR) to overcome the Nyquist limit and obtain high data efficiency. A one dimensional (1D) experiment was conducted to recover the optical fiber length; in addition, a 3D image was obtained by recovering the distances of several targets in free space. Compared to conventional methods based on fast Fourier transform (FFT), beat frequency up to 14 times the Nyquist limit for sampling frequency was successfully measured without aliasing. The proposed method dramatically increases the data efficiency in FMCW LiDAR by reducing the number of complex algorithms and experimental resources required.