To investigate the transient characteristics of high-speed axial flow water-jet pumps during start-up and emergency acceleration as well as to analyze how different accelerations affect the performance of internal flow, the k–ω turbulence model of the SST model and Zwart cavitation model were used to perform unsteady simulation on an impeller rotating at a speed of 1850. The steady-state numerical simulation method was verified by the experimental data, the numerical calculation results were basically consistent with the experimental data, the margin of error was within 5%, and the numerical simulation method was reliable. The results show that there was an obvious transient effect in the process of variable speed, and the thrust reached a stable state later than the speed. The buffer times for start-up times of 1 s, 2 s, and 3 s were 0.0394 s, 0.0375 s, and 0.0282 s, respectively, and the buffer times for the acceleration times of 0.5 s, 1.0 s, and 1.5 s were 0.0330 s, 0.0273 s, and 0.0230 s, respectively. The greater the acceleration, the more serious the flow rate and thrust lag behind the speed, and the greater the impact thrust. Under the same acceleration, the buffer time required in the start-up process was 19.3~22.6% longer than that in the acceleration process. During the change in speed of the high-speed water-jet pump, the vortex core area of the suction surface (SS) first appeared on the side of the shroud at the inlet, increased with the increase in the rotational speed, and developed toward the middle of the impeller. However, after the flow was stabilized, the vortex core region gradually shrank and eventually disappeared. When the rotational speed reached 0.6 times the design speed, cavitation occurred at the leading edge (LE) of the blade, and the cavitation area increased with the increase in the rotational speed. When reaching the same speed, the greater the acceleration, the more serious the cavitation. Under the design speed, that is, 6000 r/min, the cavitation volume fraction of the 1 s start-up process was 7.32%, the 2 s start-up process was 5.84%, the 3 s start-up process was 5.32%, and the 0.5 s acceleration process was 6.86%. The cavitation volume fraction of the 1 s acceleration process was 5.04%, and that of the 1.5 s acceleration process was 4.23%. Under the same acceleration, the cavitation volume fraction of the start-up process was 6.7~25% larger than that of the acceleration process. Compared with the start-up process and acceleration process under the same acceleration, the accelerated process had a smaller region of vortex core, stronger anti-cavitation ability, and more stable flow than the start-up process. During the actual operation process of the water-jet pump, it is advisable to use smaller accelerations and segmented accelerations as much as possible until the design speed is reached. The research findings serve as a foundation for future investigations into the transient characteristics of high-speed water-jet pumps operating under variable speed conditions.