An all-fiber refractive index (RI) sensor with a simple configuration of periodical tapers is proposed and investigated experimentally. The proposed fiber RI sensor consists of a small core fiber sandwiched between two standard singlemode fibers, with tapers periodically fabricated along the small core fiber using a focused CO2 laser beam. Such a structure can be used for RI sensing by measuring the dip wavelength shift of the multimode interference within the small core fiber cladding. An average sensitivity of 226.6 nm/RIU (RI Unit) has been experimentally achieved in the RI range from 1.33 to 1.38. The refractometer is sensitive to temperature and an experimental investigation of this sensitivity is presented. It is found that the peak shift response has a linear variation with temperature; therefore, temperature dependence can be mitigated by a suitable RI correction process. The proposed RI sensor benefits from simplicity and low cost and achieves a competitive sensitivity compared with other existing fiber-optic sensors.