1. An apparatus for measuring a blood pressure of a subject, comprising: a cuff placed around the subject's arm containing an artery; an inflating unit, coupled to the cuff, for inflating the cuff; a pressure transducer coupled to the cuff; and a controlling/processing unit, coupled to the cuff, the inflating unit and the pressure transducer, respectively, for controlling the inflating unit to inflate the cuff to an initial inflation pressure, controlling the cuff to be deflated from the initial inflation pressure, obtaining a cuff pressure signal and a sequence of raw oscillometric pulse amplitudes relating to counter-pressure of the artery from the pressure transducer as the cuff is deflated from the initial inflation pressure, calculating a respective weight for each of the raw oscillometric pulse amplitudes, correcting each of the raw oscillometric pulse amplitudes based on the weights to obtain a sequence of current oscillometric pulse amplitudes replacing the raw oscillometric pulse amplitudes, defining a maximum oscillometric pulse amplitude among the current oscillometric pulse amplitudes, determining a systolic pressure relating to the blood pressure of the subject based on the maximum oscillometric pulse amplitude, the cuff pressure signal and a first ratio, and determining a diastolic pressure relating to the blood pressure of the subject based on the maximum oscillometric pulse amplitude, the cuff pressure signal and second ratio.