When the multiphase pump is running, the internal medium often exists as bubble flow. In order to investigate the bubble occurrence characteristics in the pressurization unit of the multiphase pump more accurately, this paper couples computational fluid dynamics (CFD) with a population balance model (PBM) to investigate the bubble size distribution law of the multiphase pump under different operating conditions, taking into account the bubble coalescence and breakup. The research shows that the mean bubble size in the impeller domain gradually decreases from 1.7013 mm at the inlet to 0.6179 mm at the outlet along the axis direction; the average bubble diameter in the diffuser domain fluctuates around 0.60 mm. The bubbles in the impeller region gradually change from the trend of coalescence to the trend of breakup along the axial and radial directions, and the bubbles in the diffuser tend to be broken by the vortex entrainment. The bubble size development law is influenced by the inlet gas volume fraction (IGVF) and the rotational speed, showing a more obvious rule, where the gas phase aggregation phenomenon enhanced by the increase in IGVF promotes the trend of bubble coalescence and makes the bubble size gradually increase. The increased blade shearing effect with the increase in rotational speed promotes the trend of bubble breakup, which gradually reduces the size of the bubbles. In addition, increasing the bubble coalescence probability is a key factor leading to changes in bubble size; the bubble size development law is not very sensitive to changes in flow, and the bubble size is at its maximum under design conditions. The research results can accurately predict the performance change of the multiphase pump and provide technical guidance for its safe operation and optimal design.