Bound states in a stretched-pulse large-mode-area photonic crystal fiber mode-locking laser operating in the vicinity of zero dispersion regime is demonstrated, where the double pulse and multi-pulse bound state mode-locking are obtained. The experiment shows that the separation between sub-pulses is unequal with some randomicity. A numerical model of the mode-locked fiber laser is established and the simulations show that the laser can operate either with single-pulse or with multi-pulse in a certain pump power range depending on semiconductor saturable absorber mirror (SESAM), which selects signal randomly from noise. And the characteristic of the multi-pulse bound states and randomicity of the distance between sub-pulses are researched. The results can be used to enhance the single pulse energy, which indicated that the highest pulse energy of 19.6 nJ can be obtained with a compressed pulse duration of 76 fs and a reduced pulse energy of 11.8 nJ due to about 40% compression loss. The numerical simulation agrees well with the experiment.