A time-dependent, moving boundary, multiphase Navier-Stokes model is developed to study the effects of aqueous foam with high air-to-water volume ratio (expansion ratio, Ex) on a jet diffusion flame. The flame is formed by combusting a steady flow of propane gas. Both the shape and velocity of the foam surface are affected by evaporation and injection rates, and are obtained by volume of fluid method. The evaporation at the advancing foam front releases water vapor as well as a significant amount of air into the flame. At low foam injection rates, simulations show that the flame spreads along the foam surface and is not extinguished. This is because the injection rate is comparable to the evaporation rate, which causes cooling but prevents the foam from advancing into the flame. However, at high foam injection rates, the simulations show that the flame lifts from the burner lip and the flame is reestablished above the rising foam surface due to the continued supply of the propane gas. Thus, the foam extinguishes the flame locally in its path by increased smothering as it rises towards the top of the burner. Both the smothering and evaporation effects are found to be important.