We investigate the mass-radius relation of the neutron star (NS) with hyperons inside its core by using the Eddington-inspired Born-Infeld (EiBI) theory of gravity. The equation of state of the star is calculated by using the relativistic mean field model under which the standard SU(6) prescription and hyperon potential depths are used to determine the hyperon coupling constants. We found that, for 4×106 m2κ 6×106 m2, the corresponding NS mass and radius predicted by the EiBI theory of gravity is compatible with observational constraints of maximum NS mass and radius. The corresponding κ value is also compatible with the κ range predicted by the astrophysical-cosmological constraints. We also found that the parameter κ could control the size and the compactness of a neutron star.