The discrete dipole approximation method is used to investigate the optical extinction spectra and the electric field enhancement of Ag conical helix (CH) nanostructures. Based on an expected similarity between the radio frequency response of the antenna with the infrared and the visible response of the nanoantenna, the Ag CH nanostructures were designed as a broadband nanoantenna. It is shown that with engineering the structure parameters of the CH nanostructure the plasmonic response of the nanostructure can be designed for a desirable application. In addition, the change of the substrate material for the nanohelix growth is shown to have infinitesimal effect on the resonance peaks of the conical nanohelix. However, varying the surrounding medium can lead to considerable red-shifting of the plasmonic resonance peaks (up to 230 nm). Calculations of the near field around the helical nanoantenna show that the smaller and the larger sides of the CH are related to the plasmonic resonance peaks at low and high wavelengths, respectively. The calculation result for the extinction spectrum has also been compared with similar experimental data for a 2-pitch Ag conical nanohelix and a relatively good agreement between the numerical calculation and the experiment has been obtained.