The extinction spectra and distribution of electric near field of the octamer clusters composed of nanorings and split nanorings are calculated by using the finite-difference time-domain method (FDTD). The results show that the Fano resonances are generated in the plasmonic octamer clusters composed of nanorings and split nanorings with different incident light polarizations. In addition, multiple Fano resonances can be generated and the modulation depth and resonance wavelength of Fano resonances can be tuned by adjusting the angle of the external ring of the plasmonic octamer clusters. These results can be used in Raman scattering, biological and chemical molecule detection.