We propose and fabricate a high-sensitivity Mach-Zehnder interferometer (MZI) refractive index (RI) sensor formed by concatenating two Core-offset Joints (COJs) in a cladding-etched fiber. The two COJs are fabricated in a single-mode fiber by using a commercial fiber fusion splicer. Then, the fiber cladding is thinned by chemical etching, and high-sensitivity MZI RI sensor is formed owing to the strong interaction of the evanescent field of the thin fiber and the surrounding medium. Experimental results show that, for the MZI with a length of 10 mm and a fiber diameter of 13.2 μm, its RI sensitivities are up to 1 288.05 and 2 118.26 nm/RIU in the RI ranges of 1.333~1.368 5 and 1.368 5~1.386, respectively. The sensor reveals the advantages of high sensitivity, compact size, simple fabrication, as well as low cost.