In order to study the complex transient flow characteristics of a high-pressure aero-fuel centrifugal pump within its full working envelope, a certain type of centrifugal pump is numerically simulated, in which the simulation results are compared with the experiment results to verify the effectiveness of the present simulation method. Then, the verified simulation method is selected to analyze the transient flow characteristics, in which the time-frequency characteristic of pressure pulsation at monitored positions is analyzed by using fast fourier transform. In addition, the unsteady flow structures are studied by focusing on the relative speed, turbulent kinetic energy and so on. The results show that the main frequency of pressure pulsation in the impeller and volute is rotation frequency and blade frequency, respectively, where different monitoring points show similar trend. Meanwhile, the flow is relatively stable under design flow rate condition. However, a certain large-scale vortex appears in the impeller channel under small flow rate conditions, which mainly exists at the exit of the impeller channel near the tongue. In addition, turbulent kinetic energy at the exit of the impeller and the tongue has a large distribution range and changes seriously, where a certain hydraulic loss is produced.