We propose a refractive index insensitive temperature sensor based on hollow annular core fiber (HACF) Mach-Zehnder interferometer (MZI). The HACF is composed of a large-diameter air hole, an annular core around the air hole and a cladding. The MZI is fabricated by inserting a short section of the HACF between two short multimode fibers, and the interference occurs between the light beams transmitting along the air hole and the annular core of the HACF. Experimental results show that the MZI is insensitive to external refractive index and has temperature sensitivity of 30 pm/°C.