  In this work we consider a spacial kind of spacetime called AdS accelerating
black holes. This is a kind of black holes which contain a stringlike
singularity along polar axises attached to the black hole and it accelerates
the black hole. By using a string as a probe we study the properties of
complexity growth of black holes following the CA duality. Our result is the
growth of complexity is independent of acceleration but the string probe
detects the effects of acceleration.
