In this paper, we design a robust multi-objective track-following controller that satisfies transient response specifications and diminishes the influence of sinusoidal disturbance. To this end, a robust control problem with the multiple constraints is considered. We show that a sufficient condition satisfying the robust control problem can be expressed by linear matrix inequalities. Finally, the robust track-following controller can be designed by solving an LMI optimization problem. The effectiveness of the proposed controller design method is verified though experiments.