A hybrid no-core fiber (NCF)–graded index multimode fiber (GIMF) structure is used as a saturable absorber (SA) for mode-locked laser operation. Such an SA supports various types of soliton outputs. By changing the cavity parameters, not only the spatiotemporal mode-locking states with a stable single pulse but also tightly and loosely bound solitons are generated. Single 35.5 pJ solitons centered at 1568.5 nm have a 4 nm spectral full-width at half-maximum and an 818 fs temporal duration. Tightly bound soliton pairs with continuously tunable wavelength from 1567.48 nm to 1576.20 nm, featured with an ～700 fs pulse train with a separation of 2.07 ps, have been observed by stretching the NCF-GIMF structured device. Meanwhile, several different pulse separations from 37.57 ps to 56.46 ps of loosely bound solitons have also been realized. The results provide help in understanding the nonlinear dynamics in fiber lasers.