The three-dimensional in-nozzle flow of two single-hole injector nozzles from the engine combustion network (ECN) is investigated based on the improved multi-fluid-quasi-VOF (volume-of-fluid) solver coupled with the large-eddy simulation (LES) approach in the OpenFOAM framework. The cavitation model is also included to study the effect of the nozzle structure on the cavitation inside the nozzle and primary breakup. The continuity equations and the momentum equations are reformulated by adding the mass and momentum source terms from cavitation, respectively. Furthermore, the influence of high frequencypressure fluctuations in the pressure chamber is analyzed. The improved model is validated by comparing the simulated mass flow rates, spray momentum fluxes, discharge coefficients, and effective jet velocities with experimental values, and high consistency is obtained. In addition, the quality of the large-eddy simulation is assessed by the proportion of the resolved kinetic energy. The results demonstrate that the jet breakup process of the spray C nozzle is divided into two stages, i.e., the pre-supercavitation stage in which the jet breakup development is relatively slow and the post-supercavitation stage when the jet shatters violently. However, the jet breakup development of the spray D nozzle is much more gradual. The fluctuating injection pressure has a greater influence on the jet breakup of the spray C nozzle than that of the spray D nozzle due to the unstable cavitation.