Non-similar solution of an unsteady mixed convection flow over a vertical cone in the presence of surface mass transfer has been obtained when the axis of the cone is inline with the flow. The time dependent free stream velocity varying arbitrarily with time introduces unsteadiness in the flow field. The results have been obtained for accelerating and decelerating free stream velocities. The numerical difficulties arising at the starting point of the stream wise coordinate and for time dependent flow field are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported here to account the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different streamwise locations for various times on velocity and temperature profiles, and skin friction and heat transfer coefficients. (c) 2006 Elsevier Ltd. All rights reserved.