A simple refractive index sensor based on a Michelson interferometer in a single-mode fiber is constructed and demonstrated. The sensor consists of a single symmetrically abrupt taper region in a short piece of single-mode fiber that is terminated by ~500 nm thick gold coating. The sensitivity of the new sensor is similar to that of a long-period-grating-type sensor, and its ease of fabrication offers a low-cost alternative to current sensing applications.