The unsteady free convection flow of a non-homogeneous nanofluid over a uniformly moving vertical plate is investigated. The two imperative parameters associated with nanoparticle-based fluid mixture i.e. thermophoresis and Brownian motion effects are considered by applying Buongiorno's model with passively controlled nanoparticle concentration at the boundary. The nonlinear partial differential equations are reduced to dimensionless forms and then numerically solved using the Crank-Nicolson method. The impact of time, thermophoresis and Brownian motion on nanofluid velocity, temperature, nanoparticle concentration, local and average Nusselt numbers and skin-friction are investigated and presented. The Nusselt number is found to be enhanced with the increase of Brownian motion parameter. However, the opposite trends are observed for the thermophoresis parameter. The average skin-friction is found to be increasing with an increase in Brownian motion parameter. The present local Nusselt numbers for limiting case at different Prandtl numbers are observed to be in good agreement with the pure fluid correlation results, which verifies the accuracy of the numerical scheme. © 2019 Author(s).