  The diffusion behavior of an active Brownian particle (ABP) in polymer
solutions is studied using Langevin dynamics simulations. We find that the long
time diffusion coefficient $D$ can show a non-monotonic dependence on the
particle size $R$ if the active force $F_{a}$ is large enough, wherein a bigger
particle would diffuse faster than a smaller one which is quite
counterintuitive. By analyzing the short time dynamics in comparison to the
passive one, we find that such non-trivial dependence results from the
competition between persistence motion of the ABP and the length-scale
dependent effective viscosity that the particle experienced in the polymer
solution. \textcolor{black}{We have also introduced an effective viscosity
$\eta_{\text{eff}}$ experienced by the ABP phenomenologically. Such an active
$\eta_{\text{eff}}$ is found to be larger than a passive one and strongly
depends on $R$ and $F_{a}$}\textcolor{magenta}{.} In addition, we find that the
dependence of $D$ on propelling force $F_{a}$ presents a well scaling form at a
fixed $R$ and the scaling factor changes non-monotonically with $R$. Such
results demonstrate that active issue plays rather subtle roles on the
diffusion of nano-particle in complex solutions.
