A single scan phase contrast method for quantifying velocity in a region of interest (ROI) containing flowing spins identified prior to scanning is introduced. k-space coverage involves applying positive velocity encoding gradient pulses in acquiring odd phase encoding lines and negative velocity encoding gradient pulses in acquiring even phase encoding lines or vice versa, effectively under sampling flowing spins by a factor of two. A ghost image due to flowing spins in the ROI is formed. The ghost image is located half a field of view away from the ROI in the phase encoding direction. Prior to image acquisition, the field of view in the localizer image is adjusted so that the subsequent ghost image does not overlap with the object being imaged. Velocity quantification is done using image values in ROI and the ghost image. The proposed method is compared to conventional phase contrast in phantom and in vivo. The proposed method reduces scan time considerably.