  In this work, we present the effect of a probe string on the complexity of a
black hole according to the CA (Complexity equals action) conjecture on
Horndeski's gravity. In our system, we consider a particle moving on the
boundary of black hole spacetime in ($2+1$)-dimensions. To obtain a dual
description, we need to insertion a fundamental string on the bulk spacetime.
The effect of this string is given by the Nambu-Goto term. For the Nambu-Goto
term, we can analyze the time development of this system, which is affected by
the parameters of Horndeski's gravity. In our case, we show some interesting
complexity properties for this gravity.
