In this paper, we present an automatic beam-vector (Doppler) angle and flow velocity measurement method and implement it in pulsatile flow measurements using a clinical Doppler ultrasound system. In current clinical Doppler ultrasound flow velocity measurements, the axis of the blood vessel needs to be set manually on the B-scan image to enable the estimation of the beam-vector angle and the beam-vector angle corrected flow velocity (the actual flow velocity). In this study, an annular array transducer was used to generate a conical-shaped and symmetrically focused ultrasound beam to measure the flow velocity vectors parallel and perpendicular to the ultrasound beam axis. The beam-vector angle and flow velocity is calculated from the mode frequency (f(d)) and the maximum Doppler frequency (f(max)) of the Doppler spectrum. We develop a spectrum normalization algorithm to enable the Doppler spectrum averaging using the spectra obtained within a single cardiac cycle. The Doppler spectrum averaging process reduces the noise level in the Doppler spectrum and also enables the calculation of the beam-vector angle and flow velocity for pulsatile flows to be measured. We have verified the measurement method in vivo over a wide range of angles, from 52 degrees to 80 degrees, and the standard deviations of the measured beam-vector angles and flow velocities in the carotid artery are lower than 2.2 degrees and 12 cm/s (about 13.3%), respectively.