An integral-type sliding mode control scheme is developed that explicitly takes into account mismatched disturbances provided their bounds are known in this study. By using an integral sliding surface, the dynamics of the sliding mode is analytically obtained which does not have any reaching phase by using the integral sliding surface. To reconstruct estimates of the system states for use in a full information sliding mode control law, an asymptotic observer is also employed and the fulfillment of sliding condition, including the case when estimated states are used, is also verified. In addition, the proposed control scheme integrated with a phase leak peak filter (PLPF) is also investigated for better rejection of disturbance of narrow-band type at mid-frequency ranges in hard disk drives (HDDs). Simulation studies on track-following in HDDs are conducted to illustrate the feasibility and effectiveness of the proposed sliding mode control. They also demonstrate that the proposed scheme provides better performance than the conventional sliding mode and PID control methods.