The unsteady three-dimensional flow of nanofluid past a bi-directional stretching sheet was investigated in this paper. Effects of Brownian motion and thermophoretic diffusion of nanoparticles in the mathematical model are taking into account. The time dependent boundary layer governing equations are transformed into ordinary differential equations containing stretching parameter, unsteadiness parameter, Prandtl number, and Schmidt number. The ordinary differential equations are solved numerically. The velocity and temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters. We obtained good accuracy of the present results by comparing with the already published literature.