Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $\epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $\tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $\epsilon$. $\tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $\tau$ has a minimum as a function of the chaperone concentration. For different $\epsilon$, a nonuniversal dependence of $\tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy.