We use the results of high resolution numerical simulations to fix the theoretical model of high redshift quasars (QSO) ionizing and heating neutral gas, and predict the signal characteristics and signal/noise (S/N) ratios for Five-hundred-meter Aperture Spherical Telescope (FAST) to observe the 21cm radiation around QSO. Our conclusions are summarized as: (1) the 21cm frequency spectrum under the FAST field has full HII region for the QSO at $z=8$ and with luminosity similar to ULAS J1120+0641, while has only a small trough for the QSO at z=10 and with low luminosity; (2) the effect of Finite Light Travel Time (FLTT) obviously changes the 21cm frequency spectrum of high redshift QSOs, makes the transition curve at lower frequency much steeper than that at higher frequency; (3) the FAST telescope can observe the 21cm radiation of high redshift QSO with very high S/N ratio as high as ~ 12, thus can identify the HII regions and the FLTT effect.