The complexity of railway vehicle structures has been part of an evolutionary process for almost two hundred years. Challenges such as increased weight, increased maintenance, higher costs and energy consumption have become common. The vision for future railway vehicles is to reduce complexity, hence enable simpler structures and reduce maintenance and cost, and of course various research challenges arise from this. In fact, a number of papers in the railway engineering literature have presented practical ways to control steering of railway vehicles to improve performance. The model of the railway wheelset is highly nonlinear, mainly due to the nature of the wheelset structure and the related wheel-rail contact forces involved during operation. In this paper, the simplest design in terms of retrofitting, the actuated solid-axle wheelset is considered, we investigate actively controlled wheelsets from a Linear Parameter Varying (LPV) control aspect. We use the grid-based LPV approach to synthesize the H∞ / LPV controller, which is self-scheduled by the forward velocity, as well as the longitudinal and lateral creep coefficients. The aim of the controller is to reduce the lateral displacement and yaw angle of the wheelset. Simulation results show that the proposed controller ensures the achievement of the above targets in the considered frequency domain up to 100 rad/s.