  In low-energy effective string theory, $\alpha'$ corrections involve the
coupling of the dilaton field to Gauss-Bonnet term. We assume that the dilaton
potential is fine tuned so that the dilaton field may oscillate rapidly for a
while around the minimum of its potential but the inflation background is not
affected. By numerical method, we find that if the dilaton starts to oscillate
at the time of about $\sim 60$ e-folds before the end of inflation,
$\alpha^\prime$ correction may bring unusual oscillations to the inflationary
gravitational wave spectrum, which might be measurably imprinted in the CMB
B-mode polarization.
