A thin-walled structure of high-strength aluminum alloy 2024 (AA2024) was fabricated using novel laser and cold metal transfer and pulse (CMT-P) arc hybrid additive manufacturing (LCAHAM) technology. The influence of the wire feeding speed, scanning speed, and laser power on the forming quality was systematically studied by the response surface methodology, probability statistical theory, and multi-objective optimization algorithm. The result showed that the forming accuracy was significantly more affected by the laser power than by the wire feeding speed and scanning speed. Specifically, there was an obvious correlation between the interaction of the laser power and wire feeding speed and the resulting formation accuracy of LCAHAM AA2024. Moreover, the laser power, wire feeding speed, and scanning speed all had noticeable effects on the spattering degree during the LCAHAM AA2024 process, with the influence of the laser power surpassing that of the other two factors. Importantly, these three factors demonstrated minimal mutual interaction on spattering. Furthermore, the scanning speed emerged as the most significant factor influencing porosity compared to the wire feeding speed and laser power. It was crucial to highlight that the combined effects of the wire feed speed and laser power played an obvious role in reducing porosity. Considering the forming accuracy, spattering degree, and porosity collectively, the recommended process parameters were as follows: a wire feeding speed ranging from 4.2 to 4.3 m/min, a scanning speed between 15 and 17 mm/s, and a laser power set at approximately 2000 W, where the forming accuracy was 84–85%, the spattering degree fell within 1.0–1.2%, and the porosity was 0.7–0.9%.