Optical fiber shape sensing technology can measure three-dimensional spatial information such as attitude, orientation, track, and position. It has broad application prospects in precision interventional medicine, variant aircraft, and continuum robots. The optical frequency-domain reflectometer features high spatial resolution and distributed measurement. Compared with the wavelength-division multiplexing technology of fiber gratings, it has distinct advantages in improving the spatial resolution of shape sensing, the accuracy of shape reconstruction, and the sensing length. In this paper, the physical relationships of bending deformation with strain and wavelength shift of the Rayleigh scattering spectra of the optical fibers were established after the principle of distributed strain sensing of the optical frequency-domain reflectometer was expounded. The mathematical relationships of the bending size, bending direction, and torsion with the three orthogonal components of the spatial curve local frame were determined. Finally, the three-dimensional shape reconstruction of the optical fibers was achieved via the line integral of the tangential component. A shape sensor based on the Ni-Cr shape memory alloy wire and encapsulated by three optical fiber bundles was designed and prepared in experiments. The average maximum errors of the two-dimensional and three-dimensional shape ends are 0.58% and 3.45% of the total length of the sensor, respectively.