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Centroidal Voronoi tessellations can be constructed using iterative improvement methods such as Lloyd's method. Using iterative improvement methods implies that the convergence speed and the quality of the results depend on the initialization methods. In this paper, we propose an efficient initialization method for constructing centroidal Voronoi tessellations on surface meshes. The proposed method tries to make initial tessellations mimic the properties of the centroidal Voronoi tessellations. We compare our method with other initialization methods: random sampling, farthest point sampling and Ward's method. The results show that our method and Ward's method have the faster convergence speed than random sampling and farthest point sampling, and create better tessellations than random sampling.