  For an ordinary charged system, it has been shown that by using the
"complexity equals action" (CA) conjecture, the late-time growth rate of the
holographic complexity is given by a difference between the value of $\Phi_H
Q+\Omega_H J$ on the inner and outer horizons. In this paper, we study the
influence of the chiral anomaly on the complexity of the boundary quantum
system. To be specific, we evaluate the CA holographic complexity of the
charged supersymmetric black holes whose bulk action is modified by an
additional Chern-Simons term of the electromagnetic fields. As a result, the
late-time growth rate of the complexity will be corrected by some additional
terms on the inner and outer horizons than the ordinary charged black holes.
Our work implies that the late-time growth rate of the complexity can carry the
information of the chiral anomaly for the boundary system.
