We describe powder and single-crystal inelastic neutron scattering experiments on a spinel-type antiferromagnet GeCo2O4, represented by an effective total angular momentum Jeff=1/2. Several types of nondispersive short-range magnetic excitations were discovered. The scattering intensity maps in Q space are well reproduced by dynamical structure factor analyses using molecular model Hamiltonians. The results of analyses suggest that the molecular excitations below TN arise from molecular ground states, one of which consists of antiferromagnetically coupled ferromagnetic subunits. The quasielastic excitations above TN are interpreted as its precursor. A combination of frustration and Jeff=1/2 might induce these quantum phenomena.