A computer tomography scheme based on single-element interferometer is proposed to measure the three-dimensional refractive index distribution of optical fiber. Based on the principle of microscopic imaging, the single-element interferometer improves the lateral resolution of the system. The phase is extracted by fast Fourier transform, and the refractive index distribution of the fiber is reconstructed by filtered back projection algorithm. Based on the proposed scheme, an experimental measurement device is built to actually measure the refractive index distribution of single-mode and multimode optical fibers. The results show that the measurement can simply and quickly obtain the full optical field data, has the advantages of being lossless and non-contact, and the optical path structure is compact and stable, which provides a new idea for the miniaturization of computed tomography equipment.