In this paper, a single-mode fiber with periodically modulated tapers has been fabricated using electric arc discharge with a fiber splicer. Such a fiber with periodic tapers could effectively adjust the light propagation. The refractive index (RI) sensitivity of the proposed microfiber under different ambient RI environments has been analyzed. Experimental results show that it has an RI sensitivity of $\sim 490.9$ nm/RIU for a linear RI range from 1.3642 to 1.4015. The temperature response has also been experimentally investigated, which showing that this device possesses a low-temperature cross sensitivity, and the temperature-induced wavelength shift perturbation is <0.5 nm for an environmental temperature range of 22.5°C–80°C. Combining such desirable merits as simple fabrication procedure, compactness, low cost, and low-temperature sensitivity of the periodically modulated microfiber, this sensor is expected to find potential applications in fields, such as multi-parameter measurement and biochemical applications.