The present paper investigated the characteristics of flow and heat transfer of a Casson nanofluid boundary layer over a continuous moving surface subjected to thermal radiation and magnetic field. Nanosize particles (CuO, Ag, and Al2O3) are tested. Method of similarity transformation used to convert the governing equations of the boundary layer to a nonlinear ordinary differential equations system whose solved analytically at steady flow state and numerically at the unsteady flow boundary layer. The obtained results for the Nusselt number, skin friction, as well as for the temperature and velocity of the boundary layer for selected values of the controlling parameters. Results were compared with previously published research in some special cases and get it in a good agreement and the results were tabulated and graphs showed a good and significant effect of heat transfer by injection of the solid materials.