Abstract: An adjustable Catmull-Clark subdivision algorithm based on C-B-spline is proposed. The shape parameter α in C-B-spline is substituted by cos α, that is Ck, and the definition interval of C_k is extended to -1, ∞) in constructing the Catmull-Clark subdivision surface. When C_k is within the interval -1,1, it is a common Catmull-Clark surface built with C-B-spline, and can't reach the area between the standard Catmull-Clark surface and the original control mesh. However, as C_k is increased to over 1, the surfaces can reach this area too. This algorithm inherited nearly all properties that C-B-spline and Catmull-Clark subdivision surface possess, such as representing cylinder, and constructing surface on meshes of arbitrary topological structure etc.