Abstract: One progressive interpolation method of Catmull-Clark subdivision surface with matrix weight is presented in this paper.It aims to interpolate the normal vector of subdivision surface which normal progressive interpolation algorithm can’t make.First,a 3×3 weight matrix is presented as the weight of the given progressive interpolation method.Different matrix weights have been given in order to not only control convergence speeds and shapes but also interpolate the normal vector so as to smooth the limit surface.Second,the weight matrix can be decomposed into the sum of two matrices,one controls the convergence rate,the other controls the surface shape and smoothness.This paper also presents two different ways to determine the weight matrix.One is designing the diagonal matrix in order to control the convergence speed of x,y,z components.The other is designing the rotation matrix in order to iteratively adjust the vertex position and smooth the limit surface.At the end of this paper,a large number of numerical examples are given to demonstrate the effects of matrix weights.