  We have investigated dynamical evolution of electromagnetic perturbation in a
scalar hairy black hole spacetime, which belongs to solutions in Horndeski
theory with a logarithmic cubic term. Our results show that the parameter
$\alpha$ affects the existence of event horizon and modifies the asymptotical
structure of spacetime at spatial infinity, which imprints on the quasinormal
frequency of electromagnetic perturbation. Moreover, we find that the late-time
tail of electromagnetic perturbation in this background depends also on the
parameter $\alpha$ due to the existence of solid angle deficit. The presence of
the parameter $\alpha$ makes the perturbation field decay more rapidly. These
imply that the spacetime properties arising from the logarithmic cubic term in
the action play important roles in the dynamical evolutions of the
electromagnetic perturbation in the background of a scalar hairy black hole.
