  We study the effect of the Gauss-Bonnet term on the complexity growth rate of
dual field theory using the "Complexity--Volume" (CV) and CV2.0 conjectures. We
investigate the late time value and full time evolution of the complexity
growth rate of the Gauss-Bonnet black holes with horizons with zero curvature
($k=0$), positive curvature ($k=1$) and negative curvature ($k=-1$)
respectively. For the $k=0$ and $k=1$ cases we find that the Gauss-Bonnet term
suppresses the growth rate as expected, while in the $k=-1$ case the effect of
the Gauss-Bonnet term may be opposite to what is expected. The reason for it is
briefly discussed, and the comparison of our results to the result obtained by
using the "Complexity--Action" (CA) conjecture is also presented. We also
briefly investigate two proposals applying some generalized volume functionals
dual to the complexity in higher curvature gravity theories, and find their
behaviors are different for $k=0$ at late times.
