A Mach-Zehnder interferometer (MZI) built using several concatenated different structures is proposed as a refractive index sensor. This sensor is comprised of a microbubble, a section of reduced cladding fiber (RCF) and a core-offset single-mode fiber (SMF). These structures are joined together through specialized arc fusion splicing procedures. The sensor is characterised by immersing it in Cargille oil with refractive index values ranging from 1.30 to 1.39. The sensor exhibits linearity in respect to the refractive index changes, with a good sensitivity of 144.42 nm/RIU. The proposed MZI has the advantages of cost effective, repeatable fabrication, compact size and high sensitivity, which make it a promising sensor.