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In this paper, we mainly study large time behavior of the strong solutions tothe 2-D compressible finite extensible nonlinear elastic (FENE) dumbbell model.The Fourier splitting method yields that the $L^2$ decay rate is$\ln^{-l}(e+t)$ for any $l\in\mathbb{N}$. By virtue of the time weighted energyestimate, we can improve the decay rate to $(1+t)^{-\frac{1}{4}}$. Under thelow-frequency condition and by the Littlewood-Paley theory, we show that thesolutions belong to some Besov space with negative index and obtain the optimal$L^2$ decay rate.

Large time behavior of global strong solutions to the 2-D compressible FENE dumbbell model