In the context of global climate change and urban expansion, extreme urban weather events occur frequently and cause significant social problems and economic losses. To study the climate risks associated with rapid urbanization in the global context of climate change, the vulnerability degree of urban agglomeration is constructed by the Grey Model (GM (1, 1)). Based on the sixth phase of the Coupled Model Intercomparison Project (CMIP6) data sets SSP1-2.6, SSP2-4.5, and SSP5-8.5, drought, heat wave, and flood hazards under different emission scenarios are calculated. The vulnerability degree of the urban agglomeration and the climate change hazard were input into the climate change risk assessment model to evaluate future climate change risk. The analysis results show regional differences, with the Beijing–Tianjin–Hebei urban agglomeration having good urban resilience, the Yangtze River Delta urban agglomeration having slightly higher overall risk, and the Pearl River Delta urban agglomeration having the highest relative risk overall. On the whole, the higher the emission intensity is, the greater the risk of climate change to each urban agglomeration under different emission scenarios.