A hydrodynamic model is proposed to describe conformational relaxation of molecules, viscoelasticity of arms, and hierarchical multiple-shape memory effect (multi-SME) of hyper-branched polymer. Fox–Flory and Boltzmann’s principles are 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 is then formulated. Results reveal 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 is 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. This study is expected to provide an effective guidance on designing multi-SME in topologically hyper-branched polymers.