This work investigates mainly the double dispersion on the double diffusive convective boundary layer between a vertical plate immersed into a non-Darcy saturated porous medium with a nanofluid. The similarity transformations are involved and the governing system of nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations. Results are displayed graphically to illustrate the influence of δ, and ξ on the velocity, the temperature and concentration of the species profiles. Two interesting cases are treated, isothermal and non-isothermal wall plate. For a nanofluid, the rate of mass transfer is affected strongly by the double dispersion while the rate of heat transfer coefficient is less sensitive to it.