The research of its convergence of Mean Shift algorithm is the foundation of its application. Comaniciu and Li Xiang-ru have respectively provided the proof for the convergence of Mean Shift but they both made a mistake in their proofs. In this paper, the imprecise proofs existing in some literatures are firstly pointed out. Then, the local convergence is proved in a new way and the condition of convergence to the local maximum point is offered. Finally, the geometrical counterexamples are provided for explanation about convergence of Mean Shift and the conclusion is further discussed. The results of this paper contribute to further theoretical study and extensive application for Mean Shift algorithm.