The researches of the structural and magnetic properties of the layered chalcogenide Fe4Co3Se8, which has a ferrimagnetic order below T = 196 K, have been performed by means of X-ray diffraction, magnetic susceptibility measurements, and 59Co nuclear magnetic resonance (NMR) spectroscopy. It is found that the effective magnetic moment of iron ions is μeff ≈ 5.90(5) μB. The components of the magnetic shift and electric field gradient tensors at the Co nuclei sites have been determined. The hyperfine field induced on Co nuclei from neighboring iron ions has been estimated from the temperature dependences of the shift and susceptibility in Fe4Co3Se8. It was also established that cobalt ions in Fe4Co3Se8, as well as in the Co7Se8 compound, do not have intrinsic magnetic moment, but they do have a moment induced from neighboring iron ions ≈ 0.36(4) μB, which decreases at the magnetic ordering to 0.07(1)μB due to mutual compensation of contributions from neighboring iron ions.