This paper presents a Linear Parameter Varying (LPV) approach for automatic steering of a vehicle. The proposed gain-scheduled steering system is based on gridding the parameter space to treat the whole operating domain of longitudinal speeds. Combining a dynamical vehicle model with look-ahead dynamics, the desired closed-loop performances can be achieved for every speed using properly parameter dependent functions to satisfy the control objectives. The gain-scheduled controller is implemented and validated experimentally, and compared with a classical LPV polytopic controller, in order to assess the efficiency of the proposed approach.