  In this paper, with considering the nonlinear electromagnetic field coupled
to Einstein gravity, we obtain the higher dimensional slowly rotating charged
black hole solutions. By use of the fact that the temperature of the extreme
black hole is zero, we find that these solutions may be interpreted as black
hole solutions with inner (Cauchy) and outer (event) horizons provide that the
mass parameter $m$ is greater than an extremal value $m_{ext}$, an extreme
black hole if $m=m_{ext}$ and a naked singularity otherwise. Also, we find that
the asymptotic behavior of the spacetime is not anti deSitter for the special
values of the nonlinearity parameter. Then, we compute the ADM mass, electrical
charge, temperature, entropy, angular momentum and gyromagnetic ratio of the
solutions. Calculations of the electromagnetic field, electrical charge,
entropy and temperature showed that they are sensitive with respect to the
changing of nonlinearity parameter.
