  We examine the possible influence of Earth-directed coronal mass ejections
(ECMEs) on the Sun's shadow in the 3~TeV cosmic-ray intensity observed by the
Tibet-III air shower (AS) array. We confirm a clear solar-cycle variation of
the intensity deficit in the Sun's shadow during ten years between 2000 and
2009. This solar-cycle variation is overall reproduced by our Monte Carlo (MC)
simulations of the Sun's shadow based on the potential field model of the solar
magnetic field averaged over each solar rotation period. We find, however, that
the magnitude of the observed intensity deficit in the Sun's shadow is
significantly less than that predicted by MC simulations, particularly during
the period around solar maximum when a significant number of ECMEs is recorded.
The $\chi^2$ tests of the agreement between the observations and the MC
simulations show that the difference is larger during the periods when the
ECMEs occur, and the difference is reduced if the periods of ECMEs are excluded
from the analysis. This suggests the first experimental evidence of the ECMEs
affecting the Sun's shadow observed in the 3~TeV cosmic-ray intensity.
