To improve the research system for concurrent compound disaster vulnerability, the superimposition (reduction) effects among concurrent disasters and the different characteristics of each dimension of vulnerability were considered, and the theoretical formulas for exposure index, sensitivity index, and adaptive capacity index of the concurrent compound disaster system were derived. Moreover, a assessment index system for vulnerability of the concurrent compound disaster system was established. This system used convolutional neural networks (CNNs) to evaluate sensitivity and employed the entropy weight-TOPSIS evaluation method to evaluate exposure and adaptability, and it utilized ArcGIS technology to conduct a comprehensive assessment of system vulnerability and obtained the distribution of vulnerability grade intervals. The verification results of the avalanche-landslide example in the Guangdong-Hong Kong-Macao Greater Bay Area show that this assessment system is logically reasonable and methodologically reliable, and it has accurate assessment results, with strong scientificity and applicability. It can be effectively applied to the quantitative assessment of concurrent compound disaster vulnerability. The high and medium-high vulnerability areas of avalanche-landslide in the Guangdong-Hong Kong-Macao Greater Bay Area are concentrated in the central areas of the bay such as Yuexiu District and Tianhe District, as well as in the middle and southern areas of the bay such as Nanshan District, Futian District, and Luohu District. The districts and counties with vulnerability rankings in the top ten, such as Yuexiu District and Futian District, need to particularly consider strengthening disaster-resistant infrastructure and enhancing disaster management.