In the petroleum industry, multiphase transport pumps are a crucial technology for petroleum extraction. Therefore, the pressure fluctuation and internal-flow characteristics of multiphase transport pumps with different inlet-gas-volume fractions (IGVFs) have become an important research topic. Studying the pressure fluctuation and its effects on the performance of mixed-transport pumps under different IGVFs is significant for improving the running stability of pumps. In this work, steady and transient flow with different IGVFs was solved using the Navier–Stokes equation applied to a structured grid and the Shear Stress Transport (SST) turbulence model. The effects of IGVFs on the pressure pulsation and the performance of a three-stage, mixed-transport pump were studied. Results indicated that the numerical calculation results agreed well with the experimental data. The numerical method could predict the gas and liquid two-phase flow in the mixed-transport pump accurately. The pressure increase of this pump decreased with the increased flow quantity and the IGVFs. The efficiency improvement of the pump was limited by the increasing the flow rate. Under the rated-flow condition, a quantitative relationship was established between the relative discharge of the IGVF and the decrease in the pump head; when the IGVF exceeded 15%, the pressurization capacity decreased by more than 30%. Along the blade centerline direction, the pressure fluctuation amplitude near the suction surface of the impeller blade head gradually increased. Numerical simulation results showed that the dominant frequency of the pressure fluctuation of the impeller and diffuser was ten and seven times that of the rotation frequency, respectively. Thus, the IGVFs greatly influenced the dominant frequency of the pressure fluctuation. The air in the impeller primarily piled up at the suction surface of the blade head near the front cover. Under a centrifugal force, water was pushed to the back cover plate, making the gas-volume fraction near the front cover plate higher. Consequently, the distribution of gas content in the impeller became uneven. On the blade suction surface near the front cover plate, a low-velocity area caused by flow separation was generated, which further affected the pressure pulsation in the impeller. There were obvious vortices in the diffuser, and the vortex position had a tendency to move toward the inlet of the diffuser with an increased gas content. The flow pattern in the impeller was consistent, which indicated the great transport performance of this pump. In conclusion, through numerical simulation and experimental research, this study revealed the effects of the IGVFs on the performance and pressure pulsation of a mixed-transport pump under a gas–liquid two-phase flow condition. Our findings may serve as a guide for the optimization of a multiphase pump.