The problem of laminar boundary layer flow of magnetohydrodynamic viscoelastic radiative nanofluid, resulting from continuous stretching of an inclined sheet in the presence of thermal and nanoparticle buoyancy forces, has been investigated. Unlike traditional constant surface temperature or constant heat flux condition, convective surface boundary condition for heat transfer has been employed. With the help of appropriate similarity transforms, the governing partial differential equations (PDEs), together with boundary conditions have been transformed into a set of non-dimensional ordinary differential equations (ODEs). Approximate numerical solution for dimensionless velocity, temperature and nanoparticle concentration are obtained using the finite element method (FEM). The boundary layer flow characteristics (velocity, temperature, nanoparticle concentration, wall velocity gradient, wall temperature gradient and wall nanoparticle concentration gradient) of nanofluid for various pertinent flow parameters have been studied to get some physical insight into the flow patterns.