Mesh deformation is an important mesh editing process which provides a convenient way to modify a given mesh to meet various design requirements. Most of the existing mesh deformation methods establish their formulations in the primal vertex-based domain and are expected to produce globally smooth and consistent deformation results while preserving geometry details as much as possible. In this paper, we present a new surface-based mesh deformation method that performs the computation via an edge-based graph to increase the sampling rate for more accurate shape computation and better deformation results. The user is given the flexibility of adjusting the deformation effect between local shape preservation and global smoothness. Moreover, to simulate the deformation behaviors of regions with different materials, we introduce a stiffness property into the deformation model and present an easy and intuitive way for the user to set the material property. Experimental results demonstrate that our algorithm can produce satisfactory results and make the deformation more flexible.