Ladle metallurgy is an important steelmaking technology in high-quality steel production. The blowing of argon at the ladle bottom has been applied in ladle metallurgy for several decades. Until now, the issue of breakage and coalescence among bubbles was still far from being solved. In order to have a deep insight into the complex process of fluid flow in the gas-stirred ladle, the Euler–Euler model and population balance model (PBM) are coupled to investigate the complex fluid flow in the gas-stirred ladle. Here, the Euler–Euler model is applied to predict the two-phase flow, and PBM is applied to predict the bubble and size distribution. The coalescence model, which considers turbulent eddy and bubble wake entrainment, is taken into account to determine the evolution of the bubble size. The numerical results show that if the mathematical model ignores the breakage of bubbles, the mathematical model gives the wrong bubble distribution. For bubble coalescence in the ladle, turbulent eddy coalescence is the main mode, and wake entrainment coalescence is the minor mode. Additionally, the number of the bubble-size group is a key parameter for describing the bubble behavior. The size group number 10 is recommended to predict the bubble-size distribution.