We have experimentally observed three types of sidebands in a passively mode-locked soliton fiber laser with large anomalous dispersion for the first time to our best knowledge. By appropriately adjusting the polarization state of laser cavity, the conventional peak sidebands, peak-dip sidebands, and dip sidebands appear in the soliton spectra, respectively. The peak-dip and dip sidebands exhibit distinct characteristics from the conventional peak sidebands. The formation mechanism of the new type sidebands can be attributed to the periodic power variation. This work could help to a deeper insight of the spectrum shaping mechanism of conventional solitons.