Biodegradable cross-linkers acryloyloxyethylaminopolysuccinimide (AEA-PSI) were obtained by microwave irradiation using maleic anhydride as materials. With AEA-PSI cross-linker, cross-linked poly(N-isopropylacrylamide-co-acrylic acid) [P(NIPAAm-co-AAc)] hydrogels were prepared, and their phase transition behavior, lower critical solution temperature (LCST), water content, thermodynamics stability, and enzymatic degradation properties were investigated. By alternating the NIPAAm/AAc molar ratio, hydrogels were synthesized to have LCST in the vicinity of 37 °C. The LCST of AEA-PSI-cross-linked P(NIPAAm-co-AAc) hydrogels was significantly influenced by monomer ratio of the NIPAAm/AAc but not by the cross-linking density within the polymer network. The water content of AEA-PSI-cross-linked P(NIPAAm-co-AAc) hydrogels was more than 90% even at 37 °C, which was controlled by the monomer molar ratio of NIPAAm/AAc, swelling media, and the cross-linking density. The thermodynamics stability was also characterized by thermogravimetry. In enzymatic degradation studies, breakdown of the AEA-PSI-cross-linked P(NIPAAm-co-AAc) hydrogels was dependent on the cross-linking density.