We have experimentally obtained dispersion-managed solitons with sidebands in a passively mode-locked thulium-doped fiber laser. The stable single soliton with sidebands can be converted into two soliton pulses at the pump power of 867 mW with appropriate settings of the polarization controllers (PCs). By increasing the pump power and cautiously adjusting the PCs, the three, four, and five soliton pulses with nonuniform intensity operate with stability in the cavity due to the global soliton interaction caused by unstable continuous waves. Furthermore, the soliton bunch can be observed at the pump power of 1 W. The position of solitons in the soliton bunch is random with a fixed separation that is controllable by changing the linear phase delay. Our work gives insight into the dynamics of multipulse dispersion-managed solitons in a 2-μm mode-locked fiber laser.