Phase correction is one of the key technologies in the spectrum recovery of the Fourier transform imaging spectrometer. The present paper proposes a correction method based on simulated annealing algorithm to calculate phase error, which overcomes the disadvantage of the existing methods that can not correct the interferogram with noise. The method determines the phase optimum solution by controlling the phase decrease function, attaining objective function value by correcting interferogram data with random phase value generated in the phase range, and determining the objective function increment in accordance with the Metropolis criterion. The simulation result of the algorithm indicates that the optimized phase error is less than 0.5%, and both the error accuracy and stability of the spectrum-recovered relative spectrum is less than 1%, which is a great improvement compared with the existing algorithm.