The extinction spectrum and the electric field distribution of gold nanoring structure have been calculated and compared with those of gold nanoplate structure by using the discrete dipole approximation method. It is found that the plasmon resonance peaks can have a red-shift or blue-shift when the radius size and the shape of the nanoring change. The gold nanoring with square cross section has a largest extinction coefficient.At the main plasmon peak,the nanoring with circlar cross section has much stronger electric field and larger electric field distribution,which can serves as the surface enhanced Raman scattering substrate for biological and chemical detections.