1. A magnetic resonance imaging apparatus for imaging a coronary artery, said apparatus comprising: a pulse sequence generating unit which, in conjunction with magnetic gradient and RF field generating units, repeatedly executes and applies a data acquisition MRI pulse sequence at least twice using the same phase encoding increment on a subject to be imaged; a data acquiring unit which acquires plural sets of MRI data respectively corresponding to said repeated MRI pulse sequences using the same phase encoding increment; a heartbeat information acquiring unit which acquires heartbeat information of the subject concerning a first heartbeat and a second later occurring heartbeat; said pulse sequence generating unit using the first heartbeat information to trigger the data acquisition MRI pulse sequence within a predetermined cardiac time phase; an extracting unit which selects subsets of said plural sets of MRI data based on a predetermined cardiac time phase of the acquired second heartbeat information and from respectively corresponding time ranges by a predetermined interval measured after data acquisition backward in time from a reference cardiac time phase determined by the second heartbeat information; and a reconstructing unit which reconstructs an image of the patient's heart tissue during a predetermined cardiac time phase even if the heart rate of the patient changes by reconstructing an image from the selected subsets of MRI data.