A fast settling servo control method and apparatus for a hard disc drive and a method and apparatus estimate an acceleration coefficient of a voice coil motor (VCM) actuator suitable for the settling servo control method and apparatus for disc drives, which allow a head to stably and rapidly move to a target track when a track seek operation is performed in the hard disk drive. The settling servo control apparatus includes a state estimator which estimates position information of a head, velocity information of the head, voice coil motor (VCM) current information, and external disturbance information based on a position error signal (PES); a feedback gain multiplier which respectively multiplies the position information of the head and the velocity information of the head by predetermined feedback control gains each and outputs the multiplication results as feedback control inputs; a pulse generator which generates a pulse signal used for cancellation of slow poles with reference to at least one of initial VCM current information, initial external disturbance information, and previous control input information as well as initial position information of a head and initial velocity information of the head; and an adder which sums the feedback control inputs, the external disturbance information, and the pulse signal generated from the pulse generator and outputs the summation result to a voice coil motor (VCM) actuator as a control input.