Applied to remote sensing, a temporally and spatially modulated Fourier-transform imaging spectrometer (TSMFTIS) relies on the push broom of the flying platform to obtain an interferogram of the detected target. If the moving state of the flying platform changes during the imaging process, the target interferogram picked up from the remotely sensed image sequence will deviate from the ideal interferogram, and the recovered target spectrum will not reflect the real characteristics of the ground target object. On the basis of research on TSMFTISs, the coordinate relationship between the detector pixel and the corresponding target ground object in the photogrammetric coordinate system can be precisely described on the basis of the central projection imaging collinear equation, and the motion imaging error model of the TSMFTIS is derived using a linear spectral mixture model. The TSMFTIS motion imaging process is simulated by an actual spectrum data cube and the altitude of the airborne platform, and a sequence error image with interference fringes is acquired. Finally, an experiment is performed to validate the motion imaging error model using the TSMFTIS and a motorized stage, and the evaluation results demonstrate its feasibility.