1. A magnetic resonance imaging (MRI) apparatus comprising: an MRI sequence controller configured to perform an imaging sequence wherein imaging data is acquired after performing a pre-pulse sequence which applies a gradient magnetic field pulse for flow selection to perform one of (a) compensating a flow and (b) facilitating flow void effect in a blood vessel of an object, said imaging data being acquired by performing an MRI pulse sequence which includes a radio frequency excitation pulse and which is independent from a blood travel direction of a target blood vessel; and a blood flow image generating unit configured to generate a non-contrast-enhanced blood flow image of the object based on magnetic resonance signals acquired by the imaging sequence, wherein the MRI sequence controller is configured to control the pre-pulse sequence so that (a) the gradient magnetic field pulse for flow selection in the pre-pulse sequence is applied in a blood flow travel direction of the target blood vessel, and (b) a longitudinal magnetization recovery pulse in the pre-pulse sequence is applied after the gradient magnetic field pulse for flow selection is applied, the longitudinal magnetization recovery pulse transforming transverse magnetization of spins into longitudinal magnetization.