Purpose - The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow. Design/methodology/approach - In this case, the numerical difficulties to obtain the non-similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique. Findings - Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream-wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients. Research limitations/implications - Thermo-physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force termin themomentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to couple in this way the temperature field to the flow field. Practical implications - Convective heat transfer over a stationary cone is important for the thermal design of various types of industrial equipments such as heat exchangers, conisters for nuclear waste disposal, nuclear reactor cooling systems and geothermal reservoirs, etc. Originality/value -The combined effects of thermal diffusion and surfacemass transfer on a vertical cone has been studied. © Emerald Group Publishing Limited.