Based on the discrete dipole approximation theory, the optical properties of four kinds of cobalt nanostructures were simulated. The parameters that are the radius of cobalt nanoparticle, the atom ratio of cobalt-gold alloy, the thickness of core and shell of cobalt@gold core-shell structure, the size of hollow cobalt particles affect the extinction spectra of these structures, which were discussed. The results show that the cobalt nanoparticle with 50 nm radius has the maximal extinction efficiency; moreover the scattering efficiency excels its absorption. The extinction efficiency of hollow cobalt nanoparticle red shifts compared to that of the solid particle, and it has the maximal efficiency spectrum located at the visible region when the inner radius equals to 40 nm and the shell thickness is 5 nm. The cobalt-gold alloy with atom ratio 1 has a broad scattering spectrum in the range of visible region. The extinction spectra of cobalt@gold core-shell structure nanoparticles change from two peaks to one peak with a wider half-peak width when the thickness of the core or shell is increased. The property of cobalt@gold core-shell structure depends on the interaction of core and shell metal. These results can provide some suggestion for choosing the structural parameters in practical application, such as solar energy field.