Based on the linear response theory, the frequency and charge distributions of the plasmons in double Au atomic chain systems were studied using energy absorption spectroscopy. The results show that, in the case of the same chain length, the plasmon modes in double Au atomic chain are more prone to coupling with each other than those in single atomic chain, manifested as a single broad energy absorption peak in the single-chain system splitting into multiple sharp peaks in the double chain system, and the coupled plasmon modes exhibit opposite charge polarization directions. Furthermore, whether it is dipole or quadrupole plasmon, the frequency of the strongest energy absorption peak in double atomic chain is higher than that in single chain. The size effect of plasmons caused the frequencies of plasmons with the same order in a double chain system is lower than those in a single chain system, and in the low frequency range, there are more plasmon modes in a double chain system than in a single chain system.