With a local potential of site-impurity in the frame work of the SSH model, the Coulomb effect of the dopant ions on the vibrational modes around the charged-soliton in doped poly-acetylene has been studied. The calculated results showed that the Goldstone theorem will be destroyed and the translation mode g1 will be pined by the dopant potential. At the same time, a new even-parity mode g′ 1 has been found. The appearance of g1 and g′1 interpret well the broad peak at 930 cm-1. In addition, other localized modes have also been discussed.