In order to track the speed profile, a case study using a linear quadratic regulator (LQR) is addressed in this paper. A time-invariant nonlinear train motion model is constructed. To apply LQR, the quadratic term of the aerodynamic drag and the rolling mechanical resistance is linearized. Gradient resistance, curve resistance, and other environmental disturbance are not considered in this paper. An LQR algorithm with constraints is proposed to track a given reference speed profile. Maximum error and cumulative error are used in the evaluation of the tracking performance. The tracking results in plots, parameters tuning, and performance analysis are shown. The results show that the proposed LQR algorithm is able to track the given 1200 seconds speed profile, the cumulative error can be controlled within 4.7478m/s, and the maximum absolute error is 0.90839m/s. The output of the control variable u is also given.