A micro-fiber Mach-Zehnder interferometer (MZI), with a thousands-µm-long ring-core fiber (RCF), is demonstrated, and its performance investigation is also implemented. In this paper, the proposed MZI is manufactured by ends-splicing the short RCF segment with single-mode fiber (SMF-28), respectively. The scheme of the MZI is a typically core-mismatch structure, which has the advantages of miniaturization and simplification. Due to the core mismatch between RCF and SMF, the light from the SMF can be well separated into ring core (RC) and silica center (SC) of the RCF at the first splicing point. After transmitting through the RC and SC, the two separated light beams encounter each other and interfere at the second splicing point. Different from conventional micro-fiber MZIs using SMFs or few-mode fibers, the RCF has a higher numerical aperture, which can generate a larger optical path-length difference with a short length fiber, accumulates a higher extinction ratio and suppresses the crosstalk between the core and cladding modes. Therefore, our proposed MZI is more stable and the best extinction ratios can reach up to 18.2 dB. Meanwhile, owing to the core structure of RCF (where SC is surrounded by high-index ring core), the power propagating through low-index area of RCF is mostly confined into SC (termed the silica-center modes). These characteristics would lead to the lower sensitivity to external disturbances.