We present a new approach which allows one to insert a silica nanosphere with a single quantum dot into a high Q photonic crystal slab nanocavity with an asymmetric nanohole in the center. The high Q cavity is optimized by adjusting air holes around the L3-type cavity based on three-dimensional finite-difference time-domain simulation. High Q value of 48 700 in this asymmetric cavity is achieved. The performance of the cavity with an assumed silica sphere containing a single quantum dot in the nanohole is also discussed, in which the Q factor can reach $5\times {10}^4$ and modal volume V is $0.048{\mathrm{\mu m}}^3$ ( $\sim 0.62({\lambda }_0/n{)}^3$ ). It is found that the electric field intensity in the nanohole is much stronger than the maximum electric field in the cavity without a nanohole. This makes it possible to locate the precise position of the quantum dot with respect to the cavity mode electric maximum. This system provides a good candidate for realizing a strong interaction between a quantum dot and cavity for the study of cavity quantum electrodynamics.