  Adopting the monodromy technique devised by Motl and Neitzke, we investigate
analytically the asymptotic quasinormal frequencies of a coupled scalar field
in the Gibbons-Maeda dilaton spacetime. We find that it is described by $
e^{\beta \omega}=-[1+2\cos{(\frac{\sqrt{2\xi+1}}{2} \pi)}]-e^{-\beta_I
\omega}[2+2\cos{(\frac{\sqrt{2\xi+1}}{2}\pi)}]$, which depends on the structure
parameters of the background spacetime and on the coupling between the scalar
and gravitational fields. As the parameters $\xi$ and $\beta_I$ tend to zero,
the real parts of the asymptotic quasinormal frequencies becomes $T_H\ln{3}$,
which is consistent with Hod's conjecture. When $\xi={91/18} $, the formula
becomes that of the Reissner-Nordstr\"{o}m spacetime.
