Biodegradable and biocompatible materials with shape-memory effects (SMEs) are attractive for use as minimally invasive medical devices. Nanocomposites with SMEs were prepared from biodegradable poly(glycerol sebacate urethane) (PGSU) and renewable cellulose nanocrystals (CNCs). The effects of CNC content on the structure, water absorption, and mechanical properties of the PGSU were studied. The water-responsive mechanically adaptive properties and shape-memory performance of PGSU-CNC nanocomposites were observed, which are dependent on the content of CNCs. The PGSU-CNC nanocomposite containing 23.2 vol % CNCs exhibited the best SMEs among the nanocomposites investigated, with the stable shape fixing and shape recovery ratios being 98 and 99%, respectively, attributable to the formation of a hydrophilic, yet strong, CNC network in the elastomeric matrix. In vitro degradation profiles of the nanocomposites were assessed with and without the presence of an enzyme.