An unsteady, free convective heat and mass transfer problem of aWalters-B viscoelastic fluid non-Darcy flow over a vertical cone with the influence of thermal radiation, thermophoresis and higher-order chemical reaction has been studied. Governing equations include the continuity, momentum, energy and mass diffusion equations of the fluid. The effects of viscoelastic nature, non-Darcy parameter, porous permeability parameter, thermophoresis parameter and chemical reaction on the flow field are numerically studied by employing the implicit finite difference method of Crank-Nicolson type. Graphical display of the numerical analysis is performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number distributions. Results indicate that the thermal radiation plays a vital role in controlling the heat transfer characteristics of moving fluids, and the thermophoretic particle deposition has notable influence on the mass transfer characteristics. © 2016 by Begell House, Inc.