  We examine the $(n+1)$-dimensional $(n\geq3)$ action in which gravity is
coupled to the Born-Infeld nonlinear electrodynamic and a dilaton field. We
construct a new $(n+1)$-dimensional analytic solution of this theory in the
presence of Liouville-type dilaton potentials. These solutions which describe
charged topological dilaton black holes with nonlinear electrodynamics, have
unusual asymptotics. They are neither asymptotically flat nor (anti)-de Sitter.
The event horizons of these black holes can be an $(n-1)$-dimensional positive,
zero or negative constant curvature hypersurface. We also analyze
thermodynamics and stability of these solutions and disclose the effect of the
dilaton and Born-Infeld fields on the thermal stability in the canonical
ensemble.
