Abstract: Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, the effect of initial density fluctuations, which caused by varying the minimum distance d_\min^ between two nucleons in the initialization, on cumulants of the net-proton multiplicity distribution in Au + Au collisions at \sqrts_\rmNN^= 7.7 GeV is investigated. It is found that the density fluctuations in the initial state increase with the decrease of d_\min^ from 1.6 to 1.0 fm. During the expand of fireball, the effect of initial density fluctuations on cumulants gradually reduced, while the influence of mean-field is remarkable. In the momentum space of the final state of the collision, the influence of d_\min^ on the magnitude of the net-proton number fluctuation in a narrow pseudo-rapidity window (\varDelta \eta \leqslant 4) is negligible. However, in a broad pseudo-rapidity window (\varDelta \eta > 4), d_\min^ obviously impacts the cumulant ratios of net-proton multiplicity. In the semi-center collision (b= 5 fm), the effect of d_\min^ is about 2~3 times than that of the mean-field.