The spin dynamics of mixed-valence YbB12 has been studied by inelastic neutron scattering on a high-quality single crystal. In the Kondo-insulating regime realized at low temperature, the spectra exhibit a spin-gap structure with two sharp, dispersive, in-gap excitations at hω = 14.5 and = 20meV. The lower mode is shown to be associated with short-range correlations near the antiferromagnetic wave vector q0=(1/2, 1/2, 1/2). Its properties are in overall agreement with those expected for a "spin-exciton" branch in an indirect hybridization gap semiconductor.