  Based on the context of complexity = action (CA) conjecture, we calculate the
holographic complexity of AdS black holes with planar and spherical topologies
in Horndeski theory. We find that the rate of change of holographic complexity
for neutral AdS black holes saturates the Lloyd's bound. For charged black
holes, we find that there exists only one horizon and thus the corresponding
holographic complexity can't be expressed as the difference of some
thermodynamical potential between two horizons as that of Reissner-Nordstrom
AdS black hole in Einstein-Maxwell theory. However, the Lloyd's bound is not
violated for charged AdS black hole in Horndeski theory.
