Reverse nonequilibrium molecular dynamics and equilibrium molecular dynamics simulations were carried out to compute the shear viscosity of the pure ionic liquid system [bmim][PF6] at 300 K. The two methods yielded consistent results which were also compared to experiments. The results showed that the reverse nonequilibrium molecular dynamics (RNEMD) methodology can successfully be applied to computation of highly viscous ionic liquids. Moreover, this study provides a validation of the atomistic force-field developed by Bhargava and Balasubramanian (J. Chem. Phys. 2007, 127, 114510) for dynamic properties.