Recently, due to its superior characteristics and simple manufacture, such as small size, low loss, high sensitivity and convenience to couple, the optical fiber sensor has become one of the most promising sensors. In order to achieve the most effective realization of light propagation by changing the structure of sensors, FOM(S •Q/λres) ,which is determined by two significant variables Q-factor and sensitivity, as a trade-off parameter should be optimized to a high value. In typical sensors, a high Q can be achieved by confining the optical field in the high refractive index dielectric region to make an interaction between analytes and evanescent field of the resonant mode. However, the ignored sensitivity is relatively low with a high Q achieved, which means that the resonant wavelength shift changes non-obviously when the refractive index increases. Meanwhile, the sensitivity also leads to a less desirable FOM. Therefore, a gradient structure, which can enhance the performance of sensors by achieving high Q and high sensitivity, has been developed by Kim et al. later. Here, by introducing parabolic-tapered structure, the light field localized overlaps strongly and sufficiently with analytes. And based on a one-dimensional photonic-crystal nanofiber air-mode cavity, a creative optical fiber sensor is proposed by combining good stability and transmission characteristics of fiber and strengths of tapered structure, realizing excellent FOM ~4.7 x 105 with high Q-factors (Q~106) and high sensitivities (<700 nm/RIU).