The instability caused by the conical (or profiled) shape of a solid-axle railway wheelset can be overcome by proper design of the vehicle's primary suspension system but is generally difficult as some of the wheelset parameters, namely the conicity and creep coefficients, are time-varying. To maintain the wheelset stability at high speeds and satisfactory curving performance simultaneously over the whole range of the parameters' variations, the self-tuning linear-quadratic regulator (S-T LQR) for the primary suspension system of a high-speed two-axle railway vehicle has been developed. The objective of the controller was to minimize the lateral displacement of the wheelset relative to track centerline and its yaw angle, on straight and curved tracks. The Continuous-time Least-Absolute Error with Variable Forgetting Factor (C-T LAE+VFF) estimation algorithm has been used to estimate the wheelset parameters before being used in the calculation of the linear quadratic feedback control gain matrix. The simulation results show that the S-T LQR performed better than the fixed-gain LQR for both the conical and profiled wheelset, suggesting that the ability to estimate the time-varying wheelset parameters and use them in the feedback controller design is necessary to produce better primary suspension control performance.