We present a refractive index (RI) sensor based on a fiber Mach–Zehnder interferometer (MZI) formed by two cascaded special long-period fiber gratings (LPFGs) with rotary refractive index modulation (RLPFGs), in which the coupling occurred between the guided mode and the high-order asymmetric cladding mode. The experimental results show that the RI sensitivity of a refractometer with an interaction length of 40 mm is up to 58.8 nm/RI in the range of 1.3344 to 1.3637, which is 3.5 times higher than that of an MZI formed by two normal LPFGs. The temperature sensitivity for the same parameters of an RLPFG-MZI is about 0.03 nm/°C. Such a kind of high-sensitivity, easy-to-fabricate and simple-structure interferometer may find applications in the chemical or biochemical sensing fields.