A stability analysis is made in the context of the previously discovered
non-singular cosmological solution from 1-loop corrected superstring effective
action. We found that this solution has an instability in graviton mode, which
is shown to have a close relation to the avoidance of initial singularity via
energy condition. We also estimate the condition for the breakdown of the
background solution due to the overdominance of the graviton.Comment: 10 pages, 6 figures, revte