An atomistic simulation method is proposed for the computation of the rotational viscosity of nematic liquid crystals. The method is a non-equilibrium molecular dynamics (MD) in which the director of nematic systems is forced to rotate by an artificial force termed aligning force. A test calculation is presented for trans-4-(trans-4-n-butylcyclohexyl) cyclohexylcarbonitrile (CCH4) and very good agreement between the simulation and experiment is demonstrated.