  In this paper, we mainly study the global well-posedness and $L^2$ decay rate
for the strong solutions of the compressible co-rotation finite extensible
nonlinear elastic (FENE) dumbbell model with small initial data. This model is
a coupling of isentropic compressible Navier-Stokes equations with a nonlinear
Fokker-Planck equation. We first prove that the FENE dumbbell model admits a
unique global strong solution provided the initial data are close to
equilibrium state for $d\geq 2$. Moreover, for $d\geq3$, we show that optimal
$L^2$ decay rates of global strong solutions by the linear spectral theory.
