The static Michelson interferometer is an entity type image plane interferometer, which can solve the technical difficulty of large field of view of interferometer. In the sampling process, nonlinear interference error is introduced by the interferometer, which leads to a consequence that the spectrum cannot be recovered accurately, so the nonlinear interference error needs to be corrected. A theoretical model of nonlinear interference error is analyzed, a nonlinear interference spectrum data reconstruction algorithm is presented, and a simulation is carried out. The simulation results indicate that the target spectrum can be recovered successfully by the reconstruction algorithm with numerical fitting, and the nonlinear interference error is eliminated. The reconstruction algorithm using Cauchy dispersion formula fitting is more precise than the reconstruction algorithm using linear fitting, and the relative error between the recovery spectrum and the input spectrum is less than 0.7% at the absorption peak.