  In this paper, quartic quasi-topological black holes in the presence of a
nonlinear electromagnetic Born-Infeld field is presented. By using the metric
parameters, the charged black hole solutions of quasi-topological Born-Infeld
gravity is considered. The thermodynamics of these black holes are investigated
and I show that the thermodynamics and conserved quantities verify the first
law of thermodynamics. I also introduce the thermodynamics of asymptotically
AdS rotating black branes with flat horizon of these class of solutions and I
calculate the finite action by use of the counterterm method inspired by
AdS/CFT correspondence.
