  In this paper, the polarization modes of gravitational waves in Horndeski
gravity are studied under the Palatini formalism. After obtaining the
linearized equation of perturbations in Minkowski background, we find that the
polarization modes of gravitational waves depend on the selection of the
theoretical parameters. The polarization modes can be divided into quite rich
cases by parameters. In all cases of parameter selection, there are $+$ and
$\times$ modes propagating at the speed of light but no vector modes. The only
difference from general relativity is scalar modes, especially the scalar
degrees of freedom can be 0, 1 or 2 in different cases. The appropriate
parameter cases can be expected to be selected in the detection of
gravitational wave polarization modes by Lisa, Taiji and TianQin in the future.
