For the low precision of nonlinear spectral recovery of the Fourier transform spectrometer, a nonlinear spectral recovery method based on the fast Gaussian gridding (FGG) is studied. The theory of non-uniform Fourier transform based on FGG is studied and the simulation verifies the high recovery precision and the feasibility of the FGG method. A spectral measurement device of birefringent polarization interference is set up and the spectral recovery for the unequal-interval sampled interference signal is carried out. The spectrum recovered based on the FGG method is basically consistent with the result of spectrometer. The theoretic simulation and experimental results show that the nonlinear spectral recovery can be realized effectively by the FGG method.