  This work is devoted to establish an improved blow-up criterion for strong
solutions to a three-dimensional compressible non-Newtonian fluid with vacuum.
The considered system is the Power Law model in a bounded periodic domain in
R^3.We establish a blow-up criterion for the local strong solutions in terms of
the L^4(0,T;L^{\infty}({\Omega}))norm of the gradient of the velocity for any
power-law index q is greater than 1.
