This paper presents results from simulations of railhead wear due to initial sinusoidal and broad-band roughness using a time-domain wheel-track vertical interaction model integrated with a three-dimensional wheel-rail contact model. As typical roughness wavelengths are short and frequencies are high compared with vehicle body motions, the vehicle is simplified to an unsprung wheel mass. The rail is modelled as a Timoshenko beam discretely supported by pads, sleepers and ballast. The wheel-rail contact in the interaction model is modelled with a non-linear Hertzian contact spring. The obtained wheel-rail forces are then incorporated into the three-dimensional contact model to calculate wear over the railhead. The wheel-rail contact is modelled as non-Hertzian and non-steady based on the Variational Method [G. Xie, S.D. Iwnicki, Calculation of wear on a corrugated rail using a three-dimensional contact model, in: Proceedings of the Seventh International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Brisbane, Australia, Materials Australia, 2006] and the wear is assumed to be proportional to the friction work. Cases of both a free and a driven wheel with a constant torque are considered. The phase angles between dynamic wheel-rail force and roughness are examined and wear is found to be almost in-phase with roughness and therefore, no roughness growth is predicted by the model as presented in its current form. Although clearly in contradiction to reality where roughness grows under certain conditions this work leads to interesting question about why roughness growth is predicted by a simple contact model but not when complexity is increased to include non-Hertzian and non-steady contact conditions.