The interaction of free convection with thermal radiation of a viscous incompressible unsteady MHD flow past a moving vertical cylinder with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using an implicit finite-difference scheme of Crank-Nicolson type. Numerical results for the transient velocity, the temperature, the concentration, the local as well as average skin-friction, the rate of heat and mass transfer for various parameters such as thermal Grashof number, mass Grashof number, magnetic parameter, radiation parameter and Schmidt number are shown graphically. It is observed that, when the radiation parameter increases the velocity and temperature decrease in the boundary layer. Also, it is found that as increase in the magnetic field leads to decrease in the velocity field and rise in the thermal boundary thickness.