A high Q-factor evanescent field fiber sensor is designed based on a fiber Bragg grating (FBG) coated with carboxylic multi-walled carbon nanotubes (C-MWCNT). In a high-reflectivity FBG, multiple cladding modes are stimulated as the forward-moving guided mode within the core of the multimode fiber is coupled to the FBG’s reverse-moving guided mode within the cladding. Our evanescent field fiber sensor is highly sensitive to the refractive index without altering the architecture of fiber or deviating from the conventional process of fabricating fiber gratings. The proposed sensor exhibits a full-width at half maximum (FWHM) of 78 pm and a Q-factor of 1.9 × 104 for its standard cladding-mode resonance, outperforming the majority of reported evanescent field fiber sensors in these parameters. Furthermore, by coating C-MWCNT on the fiber sensing surface, our sensor has been demonstrated to combine multiple functions into one, such as label-free determination of human papilloma virus (HPV) DNA sequences, the measurement of different concentrations, and mispairing discrimination. The sensor design put forward offers a compelling technique within the realm of optical fiber sensing for refractive index and label-free biomolecule detection.