The extinction spectra and the electric field distributions of the cross-shaped nanostructures are calculated by the discrete dipole approximation method. Compared with the individual nanorod, the cross-shape nanostructure can generate high local electric fields at the lateral surface. Because of the electric field couplings between adjacent protruding parts, much enhanced electric fields always occur at the lateral surface of the cross-shape nanostructure, with the incident polarization direction varied. In addition, the effects of the structural parameters of the cross-shape nanostructures on their plasmonic properties are also investigated. These results would guide the preparation of the cross-shape nanostructures for their applications in surface enhanced Raman scattering.