A robust fiber-optic interferometer, which is formed by introducing two bends (i.e. z shape) to the standard telecommunication single mode fiber, is designed and analyzed theoretically and experimentally for the refractive index (RI) sensing. The first (second) bend couples (re-couples) the core (cladding) mode to the cladding (core) modes. The RI-sensitive phase difference between the core and cladding modes gives rise to the modulation of the transmitted intensity. The experimental results show that the z-shaped interferometric sensor possesses an RI sensitivity as high as 196 nm/RIU and fit well with the theoretical predictions. An investigation of the effect of perturbations of bent angle reveals that the sensor possesses relative high sensitivities as the bent angle ranges from 13° to 17° with difference between the maximum and minimum sensitivities only 2.5% indicating the structure has a good fabrication tolerance to the inaccuracy of the bent angles. In addition, the sensor has advantages of low cost, simple structure and ease of fabrication, showing great potential in many sensing applications.