  In this paper, we consider Einstein-Hilbert gravity in the presence of
cosmological constant and non-abelian nonlinear electromagnetic field of
logarithmic type which is minimally coupled to gravity. First, black brane
solution of this model is introduced and then color non-abelian DC conductivity
is calculated for this solution by using AdS/CFT duality. Our result recovers
the Yang-Mills model in $\lambda \to 0$ limit.
