A stability analysis is made in the context of the previously discover
ed non-singular cosmological solution from 1-loop corrected superstrin
g effective action. We found that this solution has an instability in
graviton mode, which is shown to have a close relation to the avoidanc
e of initial singularity via energy condition. We also estimate the co
ndition for the breakdown of the background solution due to the overdo
minance of the graviton. (C) 1998 Elsevier Science B.V. All rights res
erved.