Fourier transform spectrometer is an important instrument in the remote sensing applications. There are phase error problems in the Fourier transform spectrometer signal processing procedure. In the present paper, the cause of phase error of Fourier transform spectrometers is shown firstly. It is mainly because of inaccuracy of sampling. Then the nonlinearity of phase error is analyzed. It is suggested that it is because that the interferogram is of finite length and the interferogram is discrete that this nonlinearity exists. The authors studied this problem with a new method. The nonlinearity is shown by rigorous derivation and the authors draw the conclusion by reasoning. Then through the nonlinearity of phase error, the authors have a discussion on the possible error in the Mertz phase correcting method. The possible error lies in the phase interpolation procedure, a part of Mertz method. A method consisting of zero adding and transforming is given to reduce this error. The methods are compared and illustrated by an experiment which uses simulated interferogram from standard spectrum library. The experiment demonstrates that the method of zero adding and transforming can reduce the phase error of phase interpolation and improve the problem of rapid phase change under some circumstances, which can help get better spectrum.