The mass loss rate of the zodiacal dust cloud near the Sun has been estimated on the basis of the orbital behaviour of circumsolar dust grains suffering sublimation. It is found that the solar dust ring located at 4 solar radii from the Sun, which consists of grains whose inward spiraling due to the Poynting-Robertson effect is stopped by the influence of sublimation, loses its mass at a rate of 3.5∼0.35 tons per second.