  As in the case of Einstein or Lovelock gravity, the action of quartic
quasitopological gravity has not a well-defined variational principle. In this
paper, we first introduce a surface term that makes the variation of quartic
quasitopological gravity well defined. Second, we present the static charged
solutions of quartic quasitopological gravity in the presence of a non linear
electromagnetic field. One of the branch of these solutions presents a black
brane with one or two horizons or a naked singularity depending on the charge
and mass of the solution. The thermodynamic of these black branes are
investigated through the use of the Gibbs free energy. In order to do this, we
calculate the finite action by use of the counterterm method inspired by
AdS/CFT correspondence. Introducing a Smarr-type formula, we also show that the
conserved and thermodynamics quantities of these solutions satisfy the first
law of thermodynamics. Finally, we present the charged rotating black branes in
$(n+1)$ dimensions with $k\leq [n/2]$ rotation parameters and investigate their
thermodynamics.
