  As a quenching mechanism, AGN feedback could suppress on-going star formation
in their host galaxies. On the basis of a sample of galaxies selected from
ALFALFA HI survey, the dependence of their HI mass M[HI], stellar mass M[*] &
HI-to-stellar mass ratio M[HI]/M[*] on various tracers of AGN activity are
presented and analyzed in this paper. Almost all the AGN-hostings in this
sample are gas-rich galaxies, and there is no any evidence to be shown to
indicate that the AGN activity could increase/decrease either M[HI] or
M[HI]/M[*]. The cold neutral gas can not be fixed positions accurately just
based on available HI data due to the large beam size of ALFALFA survey. In
addition, even though AGN-hostings are more easily detected by HI survey
compared with absorption line galaxies, these two types of galaxies show
similar star formation history. If an AGN-hosting would ultimately evolve into
an old red galaxy with few cold gas, then when and how the gas has been
exhausted have to be solved by future hypotheses and observations.
