In this work, we have experimentally demonstrated the refractive index (RI) sensing characteristics of a S-shape taper refractometer (STR) based on modal interference theory. Our preliminary theoretical analysis reveals that there exists a critical cladding mode, which is essential for understanding the sensing characteristics. When the dominant cladding mode involved in a core-cladding interference is close to the critical cladding mode, the resulting RI sensitivity tends to reach a maximum value. Moreover, both the critical and the dominant cladding mode are dependent on ambient RI. Our sensor achieves a high RI sensitivity of 2109.7 nm/RIU for a transmission dip at around 1505 nm with a measurement range of 1.36 to 1.39.