Hydroxy-terminated polybutadiene was functionalized with isocyanate groups and employed in preparation of a block copolymer of polybutadiene and bisphenol A diglycidyl ether (DGEBA)-based epoxy resin. The block copolymer was characterized by Fourier transform infrared (FTIR) spectroscopy and size-exclusion chromatography (SEC). Cured blends of epoxy resin and hydroxy-terminated polybutadiene (HTPB) or a corresponding block copolymer were characterized by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMTA), and scanning electron microscopy (SEM). All modified epoxy resin networks presented improved impact resistance with the addition of the rubber component at a proportion up to 10 wt % when compared to the neat cured resin. The modification with HTPB resulted in milky cured materials with phase-separated morphology. Epoxy resin blends with the block copolymer resulted in cured transparent and flexible materials with outstanding impact resistance and lower glass transition temperatures. No phase separation was discernible in blends with the block copolymer.