Black hole echo is an important observable that can help us better understand
gravitational theories. We present that the non-linear electrodynamic black
holes can admit the multi-peak effective potential for the scalar
perturbations, which can give rise to the echoes. After choosing suitable
parameters, the effective potential can exhibit a structure with more than two
peaks. Putting the initial wave packet released outside the peaks, we find that
the time-domain profile of the echo will split when the peaks of the effective
potential change from two to three. This is a phenomenon of black hole echo and
it might be possible to determine the geometric structure of the black hole
according to this phenomenon through gravitational wave detection.
