We describe the experimental finding of three kinds of bound solitons in the Erbium-doped fiber lasers based on saturable absorber of black phosphorus. The passively mode-locked laser can obtain stretched-pulse state, double-pulse and four-pulse bound state with the sech2-shaped pulse profile. The laser can also realize Lorentzian autocorrelation trace with the duration of approximately 562 fs and deliver Lorentzian double-pulse bound state with pulse separations of approximately 5.04 ps by properly adjusting the polarization state. This project demonstrates that the same fiber laser can obtain different types of bound state pulses, which lays a foundation for further research into bound state pulses. © 2023 Elsevier Inc.