In this study, we propose a nonlinear correction method to deal with the nonlinear response produced by the infrared detectors of the Fourier transform spectrometers when the direct current (DC) signal of the interferogram is not available. Initially, the relative correction factor is derived based on the out-of-band spectrum of the spectrum that is to be corrected, and the consistency correction factor is subsequently calculated by the spectra without correction. The experimental results show that the goodness of the linear-fit curve in case of radiometric calibration can be improved from more than 0.99 to more than 0.9999 after the implementation of the proposed nonlinear correction method; further, the absolute bias of the radiance of each channel is observed to become less than 0.15 mW·m ^-2·cm·sr ^-1 after radiometric calibration. When compared with the existing correction methods, the proposed method avoids the demand from the direct-current(DC) signal of the interferogram. However, the proposed method is considerably dependent on the blackbody spectra measured at multiple temperatures during radiometric calibration. After obtaining the consistency correction factor, nonlinear correction can be achieved for any spectrum as long as the detector operates in a stable manner.