The fiber point diffraction technology is applied in interferometer to measure optical surface with high precision. The wavefront diffracted from the single mode fiber with microns core diameter can be considered as ideal spherical wave and used as the referenced wave in interferometry. To estimate the quality of diffracted wavefront, the theoretical model of optical point diffraction is introduced at first. Based on the model, the influence of fiber core diameter, deformation and end-face shape on wavefront error is studied with numerical analysis. The analysis result shows that the single mode fiber used in experiment is available for instrument design and its influence over systematic error should be negligible within certain numerical aperture. Then a point diffraction interferometer with a single fiber is designed. Compared with the double fiber system, it has merit of noise immunity, high fringe contrast and high performance. Finally, the fiber point diffraction interferometer system is put up to measure spherical surface in experiment. The interference fringes are collected and analyzed with five-step shifting, least squares unwrapping and Zernike fitting method. The results show that the interferometer with optical fiber has achieved a worthy measurement precision and has great development potential.