  Using data from ALFALFA, xGASS, HI-MaNGA and the Sloan Digital Sky Survey
(SDSS), we identify a sample of 47 "red but HI-rich"(RR) galaxies with $NUV-r >
5$ and unusually high HI-to-stellar mass ratios. We compare the optical
properties and local environments between the RR galaxies and a control sample
of "red and HI-normal"(RN) galaxies that are matched in stellar mass and color.
The two samples are similar in the optical properties typical of massive red
(quenched) galaxies in the local Universe. The RR sample tends to be associated
with slightly lower-density environments and has lower clustering amplitudes
and smaller neighbor counts at scales from several kiloparsecs to a few
Megaparsecs. The results are consistent with the RR galaxies preferentially
being located at the center of low-mass halos, with a median halo mass $\sim
10^{12}h^{-1}M_{\odot}$ compared to $\sim 10^{12.5}h^{-1}M_{\odot}$ for the RN
sample. This result is confirmed by the SDSS group catalog which reveals a
central fraction of 89% for the RR sample, compared to $\sim 60\%$ for the RN
sample. If assumed to follow the HI size-mass relation of normal galaxies, the
RR galaxies have an average HI-to-optical radius ratio of $R_{HI}/R_{90}\sim
4$, four times the average ratio for the RN sample. We compare our RR sample
with similar samples in previous studies, and quantify the population of RR
galaxies using the SDSS complete sample. We conclude that the RR galaxies form
a unique but rare population, accounting for only a small fraction of the
massive quiescent galaxy population. We discuss the formation scenarios of the
RR galaxies.
