Flame speeds in vortex rings of a stoichiometric methane/air mixture have been investigated. The flame speeds have been measured by a high-speed video camera, and the maximum tangential velocities in the vortex have been measured by a hot-wire anemometer. Results show that the flame velocity is approximately proportional to the maximum tangential velocity and its proportionality factor is about unity. By considering conservation of mass, linear momentum, and angular momentum across the flame, a simple theory has been proposed. A good agreement has been obtained between the theory and the experiment. The vortex bursting mechanism and the baroclinic torque mechanism have been discussed.