The non-linearity caused by the detector of the Fourier transform spectrometer was studied, and the influence of non-linearity on the spectrum was discussed. The quadratic non-linearity correction methods were also discussed: convolution method and iterative method. Then the two methods were used to correct the nonlinear data. A new method which is more suitable for practical data was proposed based on both convolution method and iterative method. Finally, the three methods were used to correct the non-linearity of the simulated data and the actual data. The experimental data shows that the nonlinear performance of the data after correction was restrained. And it was found that compared with the other two methods, the new method has better accuracy and faster speed.