Shape-memory epoxy resin (SMER) with strong mechanical properties have potential for a wide range of applications, but the design and synthesis of SMER with both high mechanical property and short shape recovery time are still a challenge. Hyperbranched epoxy resin shape-memory materials offer a unique approach that has been investigated by very few researchers because of the tedious synthetic process. In this work, serial hyperbranched epoxy resins with different molecular weights and structures (ETMP-n, ETHP-n, n = 6, 9, 11) were synthesized by a simple highly efficient thiol-maleimide click reaction. Cured ETHP-n films display shape fixity ratios and shape recovery ratios as high as 98.5% and 97.2% after seven shape-memory cycles, respectively. Cured ETMP-9 and ETHP-9 films demonstrate rapid response, with shape recovery times as short as 450 and 430 ms, respectively, which are significantly shorter than previously reported shape-memory epoxy resins. The maximum actuated stress of cured films reaches 0.72 MPa, which was much higher than that of most mammalian skeletal muscles (0.35 MPa). Cured ETHP-9 films exhibited higher shape-memory performances than cured ETMP-9 films because of nitrogen heterocyclic rigid structures, appropriately high crosslink density and narrower molecular weight distribution. These excellent shape-memory performances make the hyperbranched epoxy resins suitable for practical applications in microelectronic devices and artificial muscles.