  In this article, we construct exact black hole solutions with many horizons
(more than number two) in the Einstein-nonlinear electrodynamic theories. In
particular, we acquire the explicit expression of nonlinear electrodynamic
Lagrangian for the 3-horizon black holes. Then we make the investigations of
3-horizon black holes on the horizons, the null and timelike geodesics, the
Love numbers and the thermodynamics.
