The localized surface plasmon resonance of bowtie gold dimer are numerically simulated by finite element method in this work. It is found that when the geometry remains unchanged, the resonant peak shifts of gold dimer decay exponentially with increasing particle spacing, and the decay length is size-independent as the shift and gap are scaled respectively by the peak wavelength and particle size. The electric field distribution of the nanostructures under the resonance condition is further analyzed. It is found that the electric field distribution along the x and y axes of the single obeys the law of negative exponential decay, and the intensity of the electric field is related to the polarization direction of the incident electromagnetic wave. While due to the coupling effect of surface plasmon between dimers, the gap between dimers has a great influence on the attenuation rate of the electric field. Finally, the resonance absorption inensity of dimers is also studied, and it is found that the relationship between the absorption inensity and the gap of dimer is still a negative exponential function. The results of this paper have important guiding significance for micro sensing, particle capture, and so on.