The present work provides analysis of the hydro-magnetic Nanofluid boundary layer over a moving surface with variable thickness in the presence of nonlinear thermal radiation and convective boundary conditions. The governing partial differential equations system that describes the problem converted to a system of ordinary differential equations by the similarity transformation method, which solved numerically. The velocity, temperature, nanoparticles concentration of the boundary layer are plotted and investigated in details. Moreover, the surface skin friction, rate of heat and mass transfer were deduced and explained in details.