  We consider the large time behavior of global strong solutions to the
compressible viscoelastic flows on the whole space $\mathbb{R}^N\,(N\geq 2)$,
where the system describes the elastic properties of the compressible fluid.
Adding a suitable initial condition involving only the low-frequency, we prove
optimal time decay estimates for the global solutions in the $L^p$ critical
regularity framework, which are similar to those of the compressible
Navier-Stokes equations. Our results rely on the pure energy argument, which
allows us to remove the usual smallness assumption of the data in the
low-frequency.

Analysis of PDEs