We present 12CO ($J=1{ ightarrow}0$) observations of a set of local galaxies (0.04 < z < 0.08) with a large cool gas reservoir, dubbed "HI Monsters". The data were obtained using the Redshift Search Receiver (RSR) on the Five College Radio Astronomy Observatory (FCRAO) 14 m telescope. The sample consists of 20 galaxies with $M_{HI}$ > $3{ imes}10^{10}M_{odot}$ identified by the ALFALFA survey and 8 additional objects with comparable HI mass from a separate LSB galaxy study ($M_{HI}$ > $1.5{ imes}10^{10}M_{odot}$). Our sample selection is purely based on the amount of neutral hydrogen in galaxies, thereby providing a chance to study how atomic and molecular gas relate to each other in these extremely HI-rich systems. We have detected CO in 15 out of 20 ALFALFA selected HI Monsters and 4 out of 8 LSB HI Monsters. We present the global molecular gas properties of the sample and discuss how their molecular gas properties correlate with their star formation activities.