Three-dimensional (3D)-printable shape-memory polymers (SMPs) are of great interest for making advanced shape-memory materials. However, it has been challenging to combine 3D-printable capability with shape-memory function into one material. Here, we report a UV-curable epoxy with excellent shape-memory performance and improved toughness as compared with traditional epoxy counterpart. The epoxy system is realized by cross-linking epoxy resin diglycidyl ether of bisphenol F (DGEBF) ("hard" segments) with toughening agent 3-ethyl-3-oxetanemethanol (TMPO) ("soft" segments), which finally creates a three-dimensional network with TMPO-co-DGEBF block structures. The fold-deploy tests show that the shape fixity ratio (R (f)) and the shape recovery ratio (R (r)) of the epoxy with 50 wt% TMPO soft segment are above 97 and 99% even after 20 cycles of testing, respectively. In addition to bringing shape-memory performance, the toughness of the epoxy system is notably improved by the TMPO soft segments. This study provides a very promising epoxy system for 3D-printable shape-memory materials.