Moiré superlattices consisting of two-dimensional materials have attracted immense attention because of emergent phenomena such as flat band-induced Mott insulating states and unconventional superconductivity. However, the effects of spin-orbit coupling on these materials have not yet been fully explored. Here, we show that single- and double-bilayer antimony honeycomb lattices, referred to as antimonene, form moiré superlattices on a Bi(111) substrate due to lattice mismatch. Scanning tunnelling microscopy (STM) measurements reveal the presence of spectral peaks near the Fermi level, which are spatially modulated with the moiré period. Angle-resolved photoemission spectroscopy (ARPES) combined with density functional theory calculations clarify the surface band structure with saddle points near the Fermi level, which allows us to attribute the observed STM spectral peaks to the van Hove singularity. Moreover, spin-resolved ARPES measurements reveal that the observed surface states are Rashba-type spin-polarized. The present work has significant implications in that Fermi surface instability and symmetry breaking may emerge at low temperatures, where the spin degree of freedom and electron correlation also play important roles.