Neutron powder diffraction experiments reveal that Co₄Nb₂O₉ forms a noncollinear in-plane magnetic structure with CO²⁺ moments lying in the ab plane. The spin-wave excitations of this magnet were measured by using inelastic neutron scattering and soundly simulated by a dynamic model involving nearest- and next-nearest-neighbor exchange interactions, in-plane anisotropy, and the Dzyaloshinskii-Moriya interaction. The in-plane magnetic structure of Co₄Nb₂O₉ is attributed to the large in-plane anisotropy, while the noncollinearity of the spin configuration is attributed to the Dzyaloshinskii-Moriya interaction. The high magnetoelectric coupling effect of Co₄Nb₂O₉ in fields can be explained by its special in-plane magnetic structure.