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We present a novel fiber-optic refractive index (RI) sensor based on a short piece of fused-silica micro-capillary (FSC) spliced between single mode fibers (SMFs). The sensing element is the tubing wall of the FSC where multiple modes excited from the lead-in SMF interfere to form fringes that are collected by the lead-out SMF. Two types of sensors with symmetric and asymmetric structures are fabricated and tested. A single lead-in SMF is used in the symmetric structure, whereas two lead-in SMFs are used in the asymmetric structure. Experimental results show that both types of sensors have high RI sensitivities, the symmetric structure sensor has a quadrature response with a higher sensitivity in the tested RI range from 1.33 to 1.37, and the asymmetric structure has a linear RI response with a sensitivity of 580.41 nm/RIU in the same RI range. The RI sensing platform demonstrated here can be further developed as a miniaturized fiber optic biosensor for biological and biochemical analysis.