Due to their great efficiency and minimal loss, self-priming jet pumps are frequently employed in a variety of sectors for sustainable development. A short jet self-priming pump’s steady and unsteady flow characteristics are investigated numerically in this study using a standard k-ε turbulence model. The precision and dependability of the numerical calculations used in this work are demonstrated by the less than 2% difference between the pump performance data from the numerical calculation and the external characteristics test results for each flow condition. It was found that due to the perpendicularity of the nozzle axis to the impeller axis, the high-flow velocity zone in the nozzle gradually deviates to the side away from the impeller under high-flow conditions. Backflow is generated on the side close to the impeller, where eccentric vortices are created. As time progresses, the asymmetry of the low-pressure zone within the impeller becomes more pronounced under high-flow conditions, and the fluid is unable to form a stable vortex structure at a specific location. This is an important cause of impeller vibration and noise. The nonlinear vibration at the impeller inlet is less periodic, while the increase in flow rate can make the nonlinear vibration generated within the impeller more regular and stable. This reflects the fact that the fluid flow at small flow rates is more likely to be affected by the blade configuration and the shape of the flow channel, which leads to fluid instability and discontinuity. For various flow rates, the main frequency of the pressure pulsation is higher at the impeller intake (W1) than it is in the impeller channel (W2~7). Additionally, the pressure pulsation is more frequent before 10 times the rotational frequency, with no significant regularity. This suggests that the impeller and injector rear chamber dynamic and static interference impacts may have some bearing on the pressure pulsation. The pressure pulsation coefficients (W2~7) in the impeller at different flow rates show an exponentially decreasing trend with the increase of multiples of five in the rotation frequency. The equations for the relationship between CP and 5NF were obtained, respectively: CP-Q1 = 0.07044 × exp(−0.2372NF), CP-Q3 = 0.06776 × exp(−0.2564 NF), CP-Q5 = 0.07005 × exp(−0.2884 NF). The findings of this study contribute to understanding the flow inhomogeneities inside the pump as well as the analysis of the internal pump vibration, enhancing the jet pump’s efficiency and lifespan.