A new type of optical refractive-index (RI) sensor is proposed and experimentally demonstrated by using a structure of two single-mode fiber (SMF) Bragg gratings with a multimode fiber (MMF) taper in-between. The loss induced by a mismatch of waveguide structure between SMFs and MMFs is amplified by a tapering process, and is utilized for RI sensing through evanescent field. Experimental results show that the sensor possesses a tailorable sensitivity to the change of external RI and has a good linear response in the simultaneous measurement of external RI and temperature.