Astrophysical jets are ubiquitous in the universe and often associated with compact objects, and their interactions with the ambient medium not only dissipate their own energy but also provide ideal circumstances for particle acceleration. By means of theoretical analysis and particle-in-cell simulations, here we study the ion acoustic shock wave (IASW) formation and consequent ion acceleration when electron–positron (e − e +) jets are injected into ambient electron–ion plasmas. It is found that the Buneman instability can be excited first, which induces the formation of an ion acoustic wave (IAW). As the amplitude of the IAW increases, its waveform is steepened and subsequently an IASW is formed. Some ions in the ambient plasmas will be reflected when they encounter the IASW, and thus can be accelerated to form an energetic ion beam. For an initial e − e + jet with the Lorentz factor γ 0 = 100 and the ion–electron mass ratio m i /m e = 1836, the ions can be accelerated up to 580 MeV. This study deepens our understanding of the fireball model of gamma-ray bursts, the shock model of pulsar wind nebulae, the origin of cosmic rays, and other related astrophysical processes.