A novel polarization-independent fiber-optic interferometer was proposed, which was composed of a self-focusing collimator coated on the end surface and a spherical convex lens. The detection light and the reference light were arranged to propagate in the same common single-mode fiber along a common optical path, which effectively eliminates the influence of polarization fading. The micro-displacement measuring platform was built by virtue of the theoretical modeling and analysis, and a high-precision piezoelectric ceramic was adopted as a stable signal source. A real triangular wave driving voltage signal and the corresponding interference signal were measured with satisfactory results. The relationships between the displacement of piezoelectric ceramics and the driving voltage at the different scanning voltages were investigated. The experimental results show that the fiber interferometer can realize the precise measurement of small displacements. It has wide application value in the aspects of ultra-precision machine vibration measurement, micro machine, sensor and so on.