Abstract: Freeform surface design has extensive application from industrial manufacture to architecture design.In this paper,we composite the subdivision technology and the geometric partial differential equation（GPDE）methods to form a unified method for the freeform surface design.The control meshes of surfaces are triangular and quadrilateral mixed form.We choose the surface diffusion flow as the evolution equation and the finite element method coupled with a hybrid Loop and Catmull-Clark subdivision algorithm as the numerical simulation framework.We can achieve the control meshes of the hybrid subdivision surfaces through the equation evolution.Numerical experiments show that our method yields high-quality surfaces.This research presents a novel technique to constructing GPDE subdivision surfaces.