ATCA 21 cm H i observations of the rich galaxy cluster ACO 3627 in the Great Attractor region are presented . Three fields of 30 ^ { \prime } diameter located within one Abell radius of ACO 3627 were observed with a resolution of 15 ^ { \prime \prime } and an rms noise of \sim 1 mJy/beam . Only two galaxies were detected in these fields . We compare their H i distribution to new optical R-band images and discuss their velocity fields . The first galaxy is a gas-rich unperturbed spiral whereas the second shows a peculiar H i distribution . The estimated 3 \sigma H i mass limit of our observations is \sim 7 10 ^ { 8 } M _ { \odot } for a line width of 150 km s ^ { -1 } . The non-detection of a considerable number of luminous spiral galaxies indicates that the spiral galaxies are H i deficient . The low detection rate is comparable to the H i deficient Coma cluster ( Bravo-Alfaro et al . 2000 ) . ACO 3627 is a bright X-ray cluster . We therefore suspect that ram pressure stripping is responsible for the H i deficiency of the bright cluster spirals .