As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves: vertex splitting plus repeated midpoint averaging.In this paper,we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting,and generalize the strategy to arbitrary topological surfaces of general degree.By adjusting the free parameter,the proposed method can generate subdivision surfaces with flexible shapes.Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.