Mesh deformation, as an interactive shape editing and deformation technology, has important value in geometric modeling and computer animation. In recent years, detailpreserving mesh deformation techniques have been receiving much attention, such as as-rigidas- possible (ARAP) deformation. The ARAP method shows good performance in detail preservation by requiring rigidity of the local transformations of the mesh, but the alternative iterations in the optimization process needed to keep rigidity is often computationally expensive, resulting in the failure of real time mesh editing and animation when it comes to high-resolution meshes. In this paper, we propose a novel way to acquire the coarse version of the detailed highresolution mesh by constructing bi-harmonic surface on it. We implement a multi-resolution deformation framework based on the bi-harmonic surface construction and ARAP deformation. In this way, we allow the optimization process in ARAP method to run on a coarse version of the detailed mesh in order to speed up convergence. In the same time, the details of original mesh are preserved well and can be easily restored. The experiment results show that the proposed method is feasible and effective, and most importantly, the real-time performance has been greatly improved.