Screened bonding (SB), screened antibonding (SA) and charge transfer plasmon (CTP) modes in the conductively connected nanorod heterodimer are studied in detail by simulation. All of the SB, SA and CTP modes can be observed in the extinction spectra of the conductively connected nanorod heterodimer. Also, the amplitudes of the three modes can be tuned by changing the radius of the cylinder conductive connection. Even the amplitude of the SA mode can be tuned to be higher than that of the SB mode, which is difficult to achieve in an unconnected nanorod heterodimer. Furthermore, the wavelengths of the three plasmon modes can be adjusted with a high degree of freedom, since the wavelength of the SB mode mainly depends on the length of the longer nanorod, the wavelength of the SA mode mainly depends on the length of the shorter nanorod and the wavelength of the CTP mode mainly depends on the total length of the nanorod heterodimer. Our study will be helpful for the design of plasmon enhancement devices, such as surface enhanced Raman scattering (SERS), plasmon enhanced fluorescence, plasmon rulers and so on.