A series of biodegradable amphiphilic polyurethane block copolymers with hyperbranched structure were synthesized by copolymerizing poly(epsilon-caprolactone) (PCL) and poly(ethylene glycol) (PEG) together with glycerol. The copolymers were characterized, and their composition and branch length were varied with the feeding ratio between PCL, PEG, and glycerol used. Hydrogels were formed from these copolymers by swelling of water at low polymer concentrations. The hydrogels were thixotropic, and their dynamic viscoelastic properties were dependent on the copolymer composition, branch length, and polymer concentration. Hydrolytic degradation of the hydrogels was evaluated by mass loss and changes in molecular structures. The porous morphology of the hydrogels provided good permeability for gas and nutrition. Together with the tunable rheological properties, the hydrogels were found to be suitable for 3D living cell encapsulation and delivery. The morphology of the solid copolymers was semicrystalline, while the hydrogels were totally amorphous without crystallinity, providing a mild aqueous environment for living cells. When the encapsulated cells were recovered from the hydrogels followed by subculture, they showed good cell viability and proliferation ability. The results indicate that the hyperbranched copolymers hydrogels developed in this work may be promising candidates for potential injectable cell delivery application.