  The Five-hundred-meter Aperture Spherical radio Telescope (FAST) has started
the Commensal Radio Astronomy FasT Survey (CRAFTS). In this paper, we use the
technical parameters of FAST derived from commissioning observations to
simulate the completeness function for extragalactic HI survey of CRAFTS, HI
galaxies from two kinds of mock catalogues are selected. One is generated by
Monte-Carlo simulation based on the interpolated mass-velocity width function
of the ALFALFA $100\%$ (a.k.a. $\alpha$ .100) catalogue. The other is
constructed by semi-analytical N-body simulation based on the $\Lambda$CDM
model. Our results suggest that a two-pass extragalactic HI survey will be able
to detect nearly $4.8\times10^{5}$ galaxies, from which the 'faint end' slope
of the HI Mass Function (HIMF) can be recovered to $\mathrm{10^{7}\,
M_{\odot}}$ and the 'knee mass' of the HIMF can be measured to a redshift of
0.1. Considering the radio frequency interference status and sensitivity
limitation, CRAFTS will be efficient in detecting HI galaxies at redshifts
below 0.1, which implies a tremendous potential in exploring the galaxy
interactions in different environments and the spatial distribution of HI
galaxies in the local universe.
