A novel fiber-optic refractometer is proposed and demonstrated to achieve temperature- and axial strain-compensated refractive index measurement using highly sensitive outer-cladding modes in a tapered bend-insensitive fiber based Mach-Zehnder interferometer. Peak wavelength shifts associated with different spatial frequency peaks are calibrated to obtain a wavelength-related character matrix (λ)M(RI,T,ε) for simultaneous measurement of multiple environmental variables. A phase-related character matrix (Φ)M(RI,T,ε) is also acquired by direct determination of refractive index, temperature, and axial strain induced phase shifts of the corresponding sensing modes.