Abstract: Currently, the Coherent Point Drift (CPD) which based on Gaussian Mixture Model (GMM) is one of popular point pattern matching algorithms because of its robustness. However, The CPD is local optimization and its convergent rate is slower along with the size of point-set become larger. For resolving these problems, this paper presents a Global Optimal and Fast algorithm which based on CPD (GOF-CPD). The orthogonal normalization first reduce the general affine case to the orthogonal case, and the convex region boundary of the unoberserved datas log likelihood nearby the global optimal solutions are deduced by the properties of normalized point-sets. Then, the multi-start strategy based on the convex region boundary is introduced to achieve the global optimization. Finally, a new iterative scheme, called the Trust Region based global convergent SQUARed iterative EM (TR-gSQUAREM), is proposed to achieve the superlinear convergence. Experiments on both synthetic point-sets and real world data show that the proposed algorithm is efficient, speedy and robust.