When a two-dimensional Fourier transform is used, a magnetic resonance imaging apparatus has a first arithmetic unit for executing the Fourier transform in a first dimension in the repetition time interval immediately after each data acquisition or in parallel with the data acquisition, and a second arithmetic unit for executing the Fourier transform in a second dimension after all the data has been acquired. When a three-dimensional Fourier transform is used, the apparatus has a first arithmetic unit for executing the Fourier transform in a first dimension in the time interval immediately after each data acquisition or in parallel with the data acquisition, a second arithmetic unit for executing the Fourier transform in a second dimension immediately after the data acquisition of one matrix in the phase encoding direction, and a third arithmetic unit for executing the Fourier transform in a third dimension after all the data are acquired.