To develop epoxy-based shape memory polymers (ESMPs) with a high switching temperature and good mechanical and shape memory properties for deployable space structures, the crosslink density and chain flexibility of the conventional epoxy resin, diglycidyl ether of bisphenol-A, were controlled by adding a flexible epoxy resin, diglycidyl ether of ethoxylated bisphenol-A with six oxyethylene units (DGEEBA-6). With increasing DGEEBA-6 content, the crosslink density of the ESMPs increased, but their glass transition temperature (Tg) decreased. The ESMPs with suitable switching temperatures (120–135 °C) for deployable space structures showed enhanced toughness, modulus, tensile strength, elongation at break, and shape memory properties. The ESMPs had fast full recovery times of only 80 s at Tg + 20 °C. DGEEBA-6 was shown to be a good modifier of ESMPs for deployable space structures.