Spin splitting in electronic band structures via antiferromagnetic orders is a new route to control spin-polarized carriers that is available for spintronics applications. Here, we investigated the spin degrees of freedom in the electronic band structures of the antiferromagnet NdBi using laser-based spin- and angle-resolved photoemission spectroscopy (laser-SARPES). Our laser-SARPES experiments revealed that the two surface bands that appear in the antiferromagnetic state are spin polarized in opposite directions as a counterpart of the spin splitting. Moreover, we observed that the spin polarization is antisymmetric to the time-reversal invariant momentum, indicating that spin degeneracy is lifted due to the breaking of inversion symmetry at the surface. These results are well reproduced by our density functional theory calculations with the single-q magnetic structure, implying that the spin-split surface state is determined by the breaking of inversion symmetry in concert with the antiferromagnetic order.