A novel three-dimensional numerical model is proposed to investigate the effect of tool eccentricity on the coupled thermal and material flow characteristics in friction stir welding (FSW) process. An asymmetrical boundary condition at the tool-workpiece interface, and the dynamic mesh technique are both employed for the consideration of the tool eccentricity during tool rotating. It is found that tool eccentricity induces the periodical variation of the heat densities both at the tool-workpiece interface and inside the shear layer, but the fluctuation amplitudes of the heat density variations are limited. However, it is demonstrated that tool eccentricity results in significant variation of the material flow behavior in one tool rotating period. Moreover, the material velocity variation at the retreating side is particularly important for the formation of the periodic characteristics in FSW. The modeling result is found to be in good agreement with the experimental one.