A novel pH- and temperature-responsive multiblock copolymer consisting of poly(ethylene glycol) (PEG) and poly(amino-ester urethane) (PAEU) is reported. First, a biodegradable monomer, bis-1,4-(hydroxyethyl)piperazine mono-lactate (HEP mono-lactate), was synthesized by the ring-opening polymerization of D,L-lactide (LA) using HEP and $Sn(Oct)_2$ as an initiator and catalyst, respectively. The multiblock copolymers were synthesized further from PEG, HEP, HEP mono-lactate, and 1,6-diisocyanatohexamethylene (HDI) in the presence of dibutyltin dilaurate as a catalyst. The resulting copolymers were characterized by nuclear magnetic resonance spectroscopy (NMR), Fourier transform infrared spectroscopy (FTIR), and gel permeation chromatography (GPC). At pH 6.8 or higher, the copolymer aqueous solutions showed gel-to-sol transitions with increasing temperature, and the gel window covered the physiological conditions. After a subcutaneous injection of the multiblock copolymer solution into SD rats, a soft gel was formed in a short time. The degradability of the copolymer was adjusted by varying the LA content in the PAEU block.