  We study gravitational lensing in strong-field limit by a static spherically
symmetric black hole in quartic scalar field Horndeski gravity having
additional hair parameter $q$, evading the no-hair theorem. We find an increase
in the deflection angle $\alpha_D$, photon sphere radius $x_{ps}$, and angular
position $\theta_{\infty}$ that increases more quickly while angular separation
$s$ more slowly, but the ratio of the flux of the first image to all other
images $r_{mag}$ decreases rapidly with increasing magnitude of the hair $q$.
We also discuss the astrophysical consequences in the supermassive black holes
at the centre of several galaxies and note that the black holes in Horndeski
gravity can be quantitatively distinguished from the Schwarzschild black hole.
Notably, we find that the deviation $\Delta\theta_{\infty}$ of black holes in
Horndeski gravity from their general relativity (GR) counterpart, for
supermassive black holes Sgr A* and M87, for $q=-1$ respectively, can reach as
much as $25.192~\mu$as and $18.92~\mu$as while $\Delta s$ is about
$1.121~\mu$as for Sgr A* and $0.8424~\mu$as for M87*. The ratio of the flux of
the first image to all other images suggest that the Schwarzschild images are
brighter than those of the black holes in Horndeski gravity, wherein the
deviation $|\Delta r_{mag}|$ is as much as 3.082. The results suggest that
observational tests of hairy black holes in Horndeski gravity are indeed
feasible.
