Both in-phase and anti-phase two-soliton bound states are observed using the structure of step-index multimode fiber and graded-index fiber as a new saturable absorber (SA) based on nonlinear multimode interference. To our knowledge, this is the first time that results are being reported of stable bound states with a multimode fiber laser as an SA in a passively mode-locked fiber laser. The bound solitons are verified to be stable for several hours in the laser cavity when keeping the experimental environment unchanged.