A passively mode-locked erbium-doped fiber laser with a saturable absorber (SA) based on a tapered graded-index multimode fiber with zinc oxide coating is proposed and demonstrated in this paper. The device is also a platform supporting various types of solitons outputs. The conventional solitons with center wavelength of 1558.86 nm, pulse width of 537 fs, and signal-to-noise ratio of 61.27 dB are generated at the repetition frequency of 18.37 MHz. By adjusting the polarization controller and increasing pump power, tightly and loosely bound solitons and two-fold solitons can be generated. The pulse trains of tightly bound solitons exhibit the separation of 1.91 ps, the pulse width of ∼707 fs, and centered at 1560 nm, whereas the pulse separation of loose bound solitons is 18.06 ps. Such a SA is easy in fabrication and highly stable in operation and can enrich the exploration of multi-soliton complexes.