We have studied the energy spectra of polaron and the localized vibrational modes around a polaron in the weakly coupled electron-phonon systems by using an extension of SSH model that includes the second-nearest neighbor hopping interactions. The results show that (1) The electron-hole symmetry of the energy band structure is broken and the energy gap 2 Delta is slightly increased. (2) The number of localized electronic states and their location are changed as in the soliton case. (3) For a negative polaron, eight localized modes have been found, compared with seven in the previous results. (4) The energy spectra of polaron and the localized modes are related to the types of polarons by turning on the second-neighbor hopping interactions.