  We investigate the quasinormal modes of a test massless, minimally coupled
scalar field on a static and spherically symmetric black hole in the
scalar-tensor theory with field derivative coupling to the Einstein tensor,
which is a part of the Horndeski theory with the shift symmetry. In our
solution, the spacetime is asymptotically AdS (anti-de Sitter), where the
effective AdS curvature scale is determined solely by the derivative coupling
constant. The metric approaches the AdS spacetime in the asymptotic infinity
limit and precisely recovers the Schwarzschild-AdS solution in general
relativity if the coupling constant is tuned to the inverse of the cosmological
constant. We numerically find the lowest lying quasinormal frequency for the
perturbation about a test massless, minimally coupled scalar field. The
quasinormal frequency agrees with that of the Schwarzschild-AdS solution for
the tuned case. For other parameters, in the large black hole limit, as the
metric coincides with that of the Schwarzschild-AdS black hole, the quasinormal
frequency almost agrees with that of the Schwarzschild-AdS black hole and is
insensitive to the value of the cosmological constant. On the other hand, for a
small back hole the real part of the quasinormal frequency decreases as the
absolute value of the cosmological constant increases.
