The effect of thermal radiation on free convection flow in unsteady Couette motion between vertical parallel plates has been investigated subject to a time dependent temperature boundary condition at the moving plate. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Analytical solutions of the dimensionless governing equations are derived using the Laplace transform technique. The velocity and temperature profiles are shown on graphs, the variation of skin-friction, Nusselt number, volume flow rate and vertical heat flux are presented in tabular form. The effects of system parameters such as Grashof number, radiation parameter and time on the flow fields have been discussed in detail. © (2013) Trans Tech Publications, Switzerland.