Real solid systems in polymerization fluidized bed reactors (FBRs) are characterized by wide particle size distributions that change continuously due to particle micro-behavior, growth and aggregation, etc. Simulations of such gas–solid flow hydrodynamics require the solution of a coupled computational fluid dynamics (CFD)-population balance equation (PBE) model, i.e. the CFD-PBM. Therefore, the analysis of the existing numerical methods for solving the PBE is important for the ability of the numerical prediction of the coupled model. Three representatively numerical moment-based methods, namely the quadrature method of moments (QMOM), the direct quadrature method of moments (DQMOM) and the fixed pivot quadrature method of moments (FPQMOM), were used to solve the PBE for evaluating the effect of numerical method. Comparative results demonstrated the suitability of the FPQMOM for modeling polymerization FBRs with simultaneous polymerization particle growth and aggregation.