  Under the framework of the viscous chromohydrodynamics, the gluon self-energy
is derived for the quark-gluon plasma with shear viscosity. The viscous
electric permittivity and magnetic permeability are evaluated from the gluon
self-energy, through which the refraction index %in the %viscous quark-gluon
plasma is investigated. The numerical analysis indicates that the refractive
index becomes negative in some frequency range. The start point for that
frequency range is around the electric permittivity pole, and the magnetic
permeability pole determines the end point. As the increase of $\eta/s$, the
frequency range for the negative refraction becomes wider.
