The effects of electron-beam density on large-amplitude ion-acoustic waves areinvestigated in an electron-beam–plasma system with trapped electrons, using the pseudopotential method. The region of existence of ion-acoustic waves is examined, and it is shown that the conditions for their existence depend sensitively on parameters such as the electron-beam density, the electrostatic potential and the ion temperature. It turns out that a decrease in trapped electrons, an increase in beam density and a decrease in ion temperature increase the propagation speed of ion-acoustic waves, and the region of their existence spreads as the beam density decreases, the effect of trapped electrons decreases and the Mach numbers increases. New effects of electron-beam density on large-amplitude ion-acoustic waves in a plasma with trapped electrons are predicted.