In this paper, the authors propose a fast B wavelet transform method in spectrum domain and step spectrum analysis theory for extracting completed magnetic resonance(MR) spectrum data from the MR truncated data, and the reconstruction image. In this method, the feature information is abstracted from the available low-frequency MR data using B wavelet method, and then high-frequency components are exerted from the feature information and whole spectrum data is recovered by using step spectrum analysis theory(SSAT), at last MR image is reconstructed from the recovered completed spectrum data by FFT(fast Fourier transform). Experiment and simulation results show that this method gives much better reconstructed image than the available method.