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A modified first-principles-based atomistic method incorporating the anisotropic shell model is developed for the simulation of the vortex type polarization in polycrystalline ferroelectric. Based on the modified model, a series of distinct vortex and anti-vortex polarization configurations are obtained at atomic scale simulation in which the anti-vortex polarization configuration in polycrystalline ferroelectric has never been reported in the open literature. In this study, a standard definition is given to the polarized anti-vortex in mathematics and polarization topology. The accurate distribution has been obtained from the simulation and validated by analogy of the vortex field using the Landau-Ginzburg-Devonshire theory. The properties of the anti-vortex are studied to establish the relationship among the polarization value of the vector, the radius and the streamlines curvature of the anti-vortex. Based on the polarization mechanism, a method is proposed for experimenters to observe clearly and position accurately the polarization anti-vortex and vortex, which could combine as novel domain structure. Domain wall(DW) plays an important role in the domain evolution. The anti-vortex could be a special domain structure of the mixed DWs, i.e. the Ising wall and the Mixed Ising-Neel wall. Results show that the nucleation and the disappearance of the anti-vortex happen at grain boundaries(GBs) under sinusoidal electric fields loading. As the anti-vortex motion by the electric field, it is a perfect view point for the domain evolutions. It has been found that the anti-vortex core can’t pass through the GBs because of the size and disorder field. This phenomenon indicated that anti-vortex is only been obtained in grains at polycrystalline ferroelectric, and the electric field range must between-6.3 and 6.3×10~8 V/m.