Tensor decomposition of fMRI data has gradually drawn attention since it can explore the multi-way data's structure which exists inherently in brain imaging. For multi-subject fMRI data analysis, time shifts occur inevitably among different participants, therefore, shift-invariant tensor decomposition should be used. This method allows for arbitrary shifts along one modality, and can yield satisfactory results for analyzing multi-set fMRI data with time shifts of different datasets. In this study, we presented the first application of shift-invariant tensor decomposition to simulated multi-subject fMRI data with shifts of time courses and variations of spatial maps. By this method, time shifts, spatial maps, time courses, and subjects' amplitudes were better estimated in contrast to group independent component analysis. Therefore, shift-invariant tensor decomposition is promising for real multi-set fMRI data analysis.