The interaction between Au nanorods and incident light will drive free electrons to vibrate collectively on metallic surface . The phenomenon is called Surface plasmon resonance (SPR). In this thesis, Our simulation tool is three-dimensional finite-difference time-domain(3D FDTD) method, combined with Drude-critical point(Drude-CP) model for metal dispersion and convolutional perfectly matched layer(CPML) for absorbing layer. We analyze the spectral characteristic in coupled gold nanorods with different arragements, and then the explanations of the shifts of LSPR wavelength for different arrangements are presented.