The present invention provides an MR scanning method and an MRI apparatus for decreasing the artifacts while improving the signal from within the blood vessels in the parallel imaging. In the sequence for calibration data acquisition the, RF pulse of the flip angle and the slice gradient are applied, then the phase encoding pulse is applied. Thereafter the MR signal will be received while applying the read pulse with the flow compensation pulse (marked as hatch area). Using a sequence with the flow compensation added in the calibration scanning allows decreasing the artifacts caused by the blood stream. This also increased the signal from within the blood vessels, allowing improving the S/N ratio of the calibration data.