A hydrodynamic model was proposed to describe conformational relaxation of molecules, viscoelasticity of arms and hierarchical multiple-shape memory effect (multi-SME) of hyperbranched polymer. Fox-Flory and Boltzmann's principles were employed to characterize and predict the hierarchical relaxations and their multi-SMEs in hyper-branched polymers. A constitutive relationship among relaxation time, molecular weight, glass transition temperature and viscoelastic modulus was then formulated. Results revealed that molecular weight and number of arms of the topologically hyper-branched polymers significantly influence their hydrodynamic relaxations and shape memory behaviors. The effectiveness of model has been demonstrated by applying it to predict mechanical and shape recovery behaviors of hyper-branched polymers, and the theoretical results show good agreements with the experimental ones. We expect this study provides an effective guidance on designing multi-SME in topologically hyper-branched polymers.