Large Eddy Simulation(LES) of turbulent mass transfer in fully developed turbulent pipe flow has been performed to study the effect of Reynolds number on the concentration fields at $Re_{ au}=180$, 395, 590 based on friction velocity and pipe radius. Dynamic subgrid-scale models for the turbulent subgrid-scale stresses and mass fluxes were employed to close the governing equations. Fully developed turbulent pipe flows with constant mass flux imposed at the wall are studied for Sc=0.71. The mean concentration profiles and turbulent intensities obtained from the present LES are in good agreement with the previous numerical and experimental results currently available. To show the effects of Reynolds number on the turbulent mass transfer, the mean concentration profile, root-mean-square of concentration fluctuations, turbulent mass fluxes, cross-correlation coefficient, turbulent diffusivity and turbulent Schmidt number are presented.