The formation of stable single solitons and various bound states based on a graded index multimode fiber (GIMF) is investigated experimentally for the first time. Taking advantage of the principle of nonlinear multimode interference, a 143.5 cm length of GIMF is bent and two polarization controllers are used to achieve stable passive mode-locking. The spectrum of single solitons centers on 1590.5 nm with a spectral bandwidth of 3.2 nm. 976 fs of pulse duration is obtained at the repetition rate of 14.31 MHz. The maximum output power of 14.572 mW with a corresponding single-pulse energy of 1 nJ is achieved. Meanwhile, all kinds of bound states, including soliton pairs, soliton triplets, soliton quartets, and multiple-pulse bound states with different pulse separations are realized. The bound soliton with two pulses obtained has a fixed pulse interval as the incident pump power is increased. Our results suggest that a GIMF might be employed as an effective saturable absorber for ultrafast photonics applications.