Interferometric tomography can reconstruct 3D refractive index distributions through phase-shift measurements for different beam angles. To reconstruct a complex refractive index distribution, many projections along different directions are required. For the purpose of increasing the number of the projections, we earlier proposed a beam-angle-controllable interferometer with mechanical stages; however, the quality of some of extracted phase images from interferograms included large errors, because the background fringes cannot be precisely controlled. In this study we propose to apply machine learning to phase extraction, which has been generally performed by a sequence of several rule-based algorithms. In order to estimate a phase-shift image, we employ supervised learning in which input is an interferogram and output is the phase-shift image, and both are simulation data. As a result, the network after training can estimate phase-shift images almost correctly from interferograms, in which was difficult for the rule-based algorithms.