  In this paper, we are concerned with the compressible FENE dumbbell model. By
virtue of the dissipative structure and the interpolation method, we firstly
prove global regularity in $H^2$ framework for the compressible FENE system
with some large data. Then, we obtain optimal decay estimates of large
solutions in $H^1$ and remove the smallness assumption of low frequencies by
virtue of the Fourier splitting method and the Littlewood-Paley decomposition
theory. Furthermore, we establish optimal decay rate for the highest derivative
of the solutions by a different method combining time frequency decomposition
and the time weighted energy estimate. These obtained results generalize and
cover the classical results of the incompressible FENE dumbbell model.
