Shear-thinning and viscoelasticity are two non-Newtonian fluid properties widely existing in biological fluids. In this study, we found that the translation motion of a rotating particle near a wall speed up firstly, and then slows down with enhancement of fluid viscoelasticity, which is different from the behavior reported in shear thinning fluid (Chen et al. J. Fluid Mech. 2021, 927). Our research is carried out by numerical simulation of Navier-Stokes equations combined with Oldroyd-B constitutive model. This work is expected to be helpful to understand the movement of a rotating sphere near a wall in complex fluids comprehensively