The problem of thermal radiation and unsteady magnetohydrodynamic flow of a porous medium by a nanofluid past a stretching of a sheet has been investigated numerically. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. By using similarity analysis, the governing differential equations are transformed into a set of nonlinear, coupled, ordinary differential equations that are solved numerically. Numerical results are presented for velocity, temperature, and nanoparticle volume fraction profiles for different parameters of the problem as unsteadiness parameter, porous medium parameter, magnetic field parameter, local Rayleigh number, buoyancy-ratio parameter, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter, nanoparticle buoyancy parameter, and heat source/sink parameter, etc. Also, the effects of the pertinent parameters on skin friction, rate of heat transfer, and mass fluxes are obtained and discussed numerically and illustrated graphically