The diffusion of polymer chains in crowded environments with immobile, attractive nanoparticles (NPs) is studied using the Langevin dynamics simulation approach. Simulations are performed for sufficiently long polymer chains and high enough volume fractions of NPs so that the polymer chains can be in contact with two or more NPs simultaneously. For orderly distributed NPs in specific lattices, normal diffusion with a linear increase of mean-squared displacement (MSD) with time is observed. When positional disorder of NPs is introduced by displacing NPs from lattice sites, subdiffusion with a nonlinear increase of MSD with time is observed at a sufficiently large positional disorder of NPs. The transition from the normal diffusion to the subdiffusion is attributed to the change of the energy barrier that obstructs the move of a polymer between different NPs or NP clusters. The energy barrier increases with increasing positional disorder. At high positional disorders, polymers will be trapped within NP clusters for a very long time and thus exhibit intermittent motion suggestive of continuous-time random walk (CTRW) behavior, and subdiffusive behavior is observed.