A numerical study is carried out for the magnetohydrodynamics (MHD) convective stagnation point flow of a incompressible nanofluid towards a stretching surface. The effects of Brownian motion and thermophoresis are incorporated for the characteristic of the nanofluid. The transformed dimensionless governing equations are solved directly by the collocation spectral method (CSM). Graphical results are presented and analyzed for non-dimensional velocities, temperature and nanoparticle concentration. The effects of Prandtl number, magnetic field, viscous dissipation, heat source/sink with suction/injection, Lewis number, thermophoresis parameters and Brownian motion parameter, etc., on flow, thermal and concentration boundary layer as well as on skin-friction coefficient, local Nusselt number and Sherwood number are obtained and discussed. The two-dimensional irregular characteristics have been found in the velocity and temperature distributions in the flow and normal directions. (C) 2018 Elsevier Ltd. All rights reserved.