  String cosmology models predict a relic background of gravitational-wave (GW)
radiation in the early universe. The GW energy spectrum of radiated power
increases rapidly with the frequency, and therefore it becomes a potential and
meaningful observation object for high-frequency GW detector. We focus on the
stochastic background generated by superinflation in string theory and search
for such signal in the observing data of Advanced LIGO and Virgo O1$\sim$O3
runs in a Bayesian framework. We do not find the existence of the signal, and
thus put constraints on the GW energy density. Our results indicate that at
$f=100\,\text{Hz}$, the fractional energy density of GW background is less than
$1.7\times10^{-8}$ and $2.1\times10^{-8}$ for dilaton-string and dilaton only
cases respectively, and further rule out the parameter space restricted by the
model itself due to the non-decreasing dilaton and stable cosmology background
($\beta$ bound).
