A system and method for the acquisition of preferential arterial and venous images is disclosed. The invention includes setting a noise level in the phase image, that is proportional to the velocity encoding value, at a threshold level above the venous signal but below the arterial signal during a systolic portion of the cardiac cycle and acquiring a phase contrast MR image during the systolic portion that effectively acquires the arterial signal and suppresses the venous signal. During the diastolic portion of the same R—R interval, the velocity encoding value is then set to establish a noise threshold level in the phase image lower to a value below the venous signal but above the arterial signal to acquire the venous signal and suppress the arterial signal. In this manner, either an arterial only image or a venous only image can be displayed. Alternatively, the images can be combined to create a higher SNR arterial and venous image.