In this paper, firstly, the applicability of the differential quadrature method (DQM) as an efficient and accurate numerical method for solving the problem of variable viscosity and thermally radiative unsteady magneto-hydrodynamic (MHD) flow over a moving vertical plate with suction and heat flux is investigated. The spatial as well as the temporal domains are discretized using the DQM. The fast rate of convergence of the method is demonstrated and for the cases that a solution is available, comparison is done. Then, effects of the temperature dependence of viscosity and different fluid parameters on the velocity and temperature of transient MHD flow subjected to the above mentioned boundary condition are studied. (C) 2010 Elsevier Ltd. All rights reserved.