A series of PDAAM-co-PNIPAM-co-Mu copolymers were synthesized by RAFT polymerization from diacetone acrylamide (DAAM), N-isopropylacrylamide (NIPAM) and ureidopyrimidinone-containing monomer (Mu). Their structure and composition were characterized by Nuclear Magnetic Resonance (1H-NMR) and Gel Permeation Chromatography (GPC). Smart hydrogels crosslinked with acylhydrazone reversible covalent bonds were obtained by the reaction between PDAAM-co-PNIPAM-co-Mu and adipic dihydrazide (ADH). Due to the introduction of ureidopyrimidinone (UPy) hydrogen-bonding units into the network, the mechanical properties of the hydrogels were reinforced, and the compression strength of the hydrogel was increased by ca. 4 times. Meanwhile, the hydrogels exhibited pH and temperature dual-responsive and self-healing properties, and the compression strength was increased by ca. 30 times after heating.