We propose and investigate an ultra-compact air-mode photonic crystal nanobeam cavity (PCNC) with an ultra-high quality factor-to-mode volume ratio (Q/V) by quadratically tapering the lattice space of the rectangular holes from the center to both ends while other parameters remain unchanged. By using the three-dimensional finite-difference time-domain method, an optimized geometry yields a Q of 7.2×106 and a V∼1.095(λ/nSi)3 in simulations, resulting in an ultra-high Q/V ratio of about 6.5×106(λ/nSi)-3. When the number of holes on either side is 8, the cavity possesses a high sensitivity of 252 nm/RIU (refractive index unit), a high calculated Q-factor of 1.27×105, and an ultra-small effective V of ∼0.758(λ/nSi)3 at the fundamental resonant wavelength of 1521.74 nm. Particularly, the footprint is only about 8×0.7 μm2. However, inevitably our proposed PCNC has several higher-order resonant modes in the transmission spectrum, which makes the PCNC difficult to be used for multiplexed sensing. Thus, a well-designed bandstop filter with weak sidelobes and broad bandwidth based on a photonic crystal nanobeam waveguide is created to connect with the PCNC to filter out the high-order modes. Therefore, the integrated structure presented in this work is promising for building ultra-compact lab-on-chip sensor arrays with high density and parallel-multiplexing capability.