The problem of wellbore leakage is a key challenge in the petroleum industry, limiting drilling progress and increasing drilling costs. Plugging agents play a role in repairing leaks and fractures; however, traditional plugging materials generally have low mechanical strength, poor adaptability to permeable strata, limited water absorption and expansion capabilities, and poor temperature and salt resistance. To address these limitations, a pioneering polyacrylic acid-polyacrylamide (PAA/PAM) double-network hydrogel was synthesized through aqueous solution polymerization in this study. Its strength, water absorption, expansion, temperature resistance, salt resistance, and plugging effectiveness were comprehensively evaluated. The results demonstrate that good mechanical performance is exhibited by the synthesized hydrogel, capable of withstanding a maximum stress of approximately 3.5 MPa at a 90% strain. Excellent water absorption and expansion are observed in the synthesized double-network hydrogel, with a maximum expansion of 6 times within 30 min and 8 times after 2 h. Test results show that the hydrogel had good temperature resistance and salt resistance, maintaining a strength grade E within the experimental range. The simulated evaluation of the plugging experiment indicates that, under conditions of 130 °C and 6 MPa, the leakage rate of the drilling fluid is maintained below 5 mL/min when the double-network hydrogel is utilized. From the above experimental results, it can be illustrated that excellent mechanical properties, impressive water absorption, and expansion capabilities are exhibited by the synthesized double-network hydrogel. Furthermore, the high-temperature resistance and salt resistance of the double-network hydrogel were also demonstrated. Therefore, In comparison to traditional plugging materials, significant promise is held by this newly synthesized double-network hydrogel material as a plugging agent in drilling fluids.