A gold dimer structure consisting of a notched triangle nanoslice and a rectangle nanorod is proposed to produce distinct Fano resonance. Owing to the coupling between the dipole plasmon mode of the nanorod and the dipole or quadrupole plasmon mode of the nanoslice, the extinction spectrum with a deep Fano dip is formed and can be well fitted by the Fano interference model for different geometry parameters. In addition, Fano resonance of the gold dimer nanostructure also intensely depends on the polarization direction of incident light. Moreover, Fano resonance of the triangle–rod trimer is also analyzed by adding another nanorod into the former dimer and exhibits the splitting of plasmonic resonant peak in high order coupling modes. The plasmonic hybridizations in these nanostructures have been analyzed for revealing the physical origin of the Fano resonance.