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The thermal and velocity slips of boundary layer of Williamson nanofluid over a stretching sheet are studied numerically. Buongiorno model is used to explore the heat transfer phenomena caused by Brownian motion and thermophoresis. Using similarity transformations, the governing equations are reduced to a set of nonlinear ordinary differential equations (ODEs). These equations are solved numerically by using Shooting method. The effects of non-Newtonian Williamson parameter, velocity and thermal slip parameters, Prandtl number, Brownian parameter, Schmidt number, Lewis number, Brownian motion parameter, thermophoresis parameter on velocity, temperature and concentration fields are shown graphically and discussed. The results found that the thickness of boundary layer decreases as the slip and thermal factor parameter increases. Further, present results indicate that the nanofluid temperature and concentration are enhanced with a rise of Williamson parameter. The Nusselt number is reduced with an increase of the Lewis and Prandtl numbers.