The solubility of dissolved greenhouse gas (GHG), such as carbon dioxide (CO₂) and methane (CH₄) in water will be decreased under discharge conditions due to the sudden change of pressure, which will lead to gas-liquid mass transfer and GHG emission. However, the research about GHG emission under flood discharge conditions is still rare. Considering the limitation of prototype observation and model experiment, a mathematical model for GHG emission rate under flood discharge conditions was built in this paper. The model is based on the VOF (volume of fluid) method and takes into account the bubble mass transfer and free surface mass transfer. We simulated the transport and diffusion of dissolved CO₂ and CH₄ in the spillway and jet flow respectively, and calculated their concentration distribution and emission rate. The simulated results show that the concentration distribution of GHG downstream of the dam is mainly affected by the upstream inflow concentration, gas-liquid mass transfer, the transport and diffusion of dissolved GHG. Among them, the concentration of GHG in the upstream flow is the main factor affecting the emission rate downstream of the dam. This study provides a new research approach and technical base for clarifying the amount of GHG emission rate under different discharge types, and scientifically evaluating the hydroelectric carbon footprint.