The onset of convective instability in a layer of porous medium saturated by the Oldroyd-B viscoelastic nanofluid heated from below is investigated by incorporating the effects of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticles is taken to be zero on the boundaries. The resulting eigenvalue problem is solved numerically using the Galerkin method. The onset of convective instability is oscillatory only if the strain retardation parameter is less than the stress relaxation parameter and also when the strain retardation parameter does not exceed a threshold value which in turn depends on other physical parameters. The oscillatory onset is delayed with increasing strain retardation parameter, while an opposite trend is noticed with increasing stress relaxation parameter. The effect of increasing modified diffusivity ratio, concentration Darcy-Rayleigh number, modified particle density increment and Lewis number is to hasten the onset of stationary and oscillatory convection and also to decrease the ranges of the strain retardation parameter within which oscillatory convection is preferred. (C) 2015 Elsevier Ltd. All rights reserved.