In a method and apparatus for MR imaging, a data acquisition sequence is executed wherein at least two slices of an examination subject are imaged in parallel with a gradient echo method for spatially resolved quantification of the T1 relaxation time. At least one first acquisition sequence is implemented to acquire MR data from a first slice of the examination subject and at least one second acquisition sequence is implemented to acquire MR data from a second slice of the examination subject. The acquisition sequences each include an inversion pulse and at least two successive readout steps. The first and second acquisition sequences are temporally offset from one another such that they at least partially overlap.