We demonstrate the existence of the spin-nematic interactions in an easy-plane type antiferromagnet Ba2CoGe2O7 by exploring the magnetic anisotropy and spin dynamics. The combination of neutron scattering and magnetic susceptibility measurements reveals that the origin of the in-plane anisotropy is an antiferro-type interaction of the spin-nematic operator. The relation between the nematic operator and the electric polarization in the ligand symmetry of this compound is presented. The introduction of the spin-nematic interaction is useful to understand the physics of spin and electric dipole in multiferroic compounds.