This paper presents zero crossing point(ZCP) estimation methods considering discretization error for a high speed brushless DC(BLDC) motor drive. The ZCP is estimated by detecting the change of back-EMF polarity for the BLDC sensorless drive, and the discretization error exist on the estimated ZCP. The discretization error of the ZCP is a cause of the delay of a commutation timing of current and increment of a current ripple factor. Besides a delay of a ZCP estimation brings on the limitation of a speed range for the BLDC sensorless drive. The compensation method based on the error analysis with probability theory for reducing the effects of the discretization error of the ZCP is proposed. Also a ZCP estimation method according to the Back-EMF patterns is proposed to widen the speed range for the BLDC sensorless drive. The proposed methods are verified by the experiment.