Faraday tomography provides pivotal information on the magnetoionic media along the line of sight through the Faraday dispersion function (FDF). Observing the magnetoionic media oﬀer insight on to magnetized astronomical objects, such as quasars, galaxies or intergalactic medium in galaxy clusters. The FDF can be obtained by the inverse Fourier transform of the observed linear polarization spectrum. However, the transform gives an insuﬃcient reconstruction of the FDF because the instrument limits the observable wavelength coverage. Up to now, the inability to solve the above inverse problem reliably has noticeably plagued cosmic magnetism studies. Inspired by the well-studied area of signal restoration, we propose the Constraining and Restoring iterative Algorithm for Faraday Tomography (CRAFT). The iterative technique is computationally inexpensive and only initially requires weak physicallymotivated assumptions to produce high ﬁdelity FDF reconstructions. We demonstrate the reconstruction algorithm for a realistic synthetic model FDF of the Milky Way, and the results show that our technique considerably outperforms other popular reconstruction techniques. The spectral dependence on the diﬀerent methods is also demonstrated with a simpler FDF. The proposed approach will be critical for future cosmic magnetism studies, especially with broadband polarization data from the Square Kilometre Array and its precursors.