  In this paper, we construct a new class of charged rotating dilaton black
brane solutions, with complete set of rotation parameters, which is coupled to
a nonlinear Maxwell field. The Lagrangian of the matter field has the form of
the power-law Maxwell field. We study the causal structure of the spacetime and
its physical properties in ample details. We also compute thermodynamic and
conserved quantities of the spacetime such as the temperature, entropy, mass,
charge, and angular momentum. We find a Smarr-formula for the mass and verify
the validity of the first law of thermodynamics on the black brane horizon.
Finally, we investigate the thermal stability of solutions in both canonical
and grand-canonical ensembles and disclose the effects of dilaton field and
nonlinearity of Maxwell field on the thermal stability of the solutions. We
find that for $\alpha \leq 1$, charged rotating black brane solutions are
thermally stable independent of the values of the other parameters. For
$\alpha>1$, the solutions can encounter an unstable phase depending on the
metric parameters.
