Aerobic granulation is a promising process for wastewater treatment, but this granulation process is very complicated and is affected by many factors. Thus, a mathematical model to quantitatively describe such a granulation process is highly desired. In this work, by taking into account all of key steps including biomass growth, increase in particle size and density, detachment, breakage and sedimentation, an one-dimensional mathematic model was developed to simulate the granulation process of activated sludge in a sequencing batch reactor (SBR). Discretization methodology was applied by dividing operational time, sedimentation process, size fractions and slices into discretized calculation elements. Model verification and prediction for aerobic granulation process were conducted under four different conditions. Four parameters indicative of granulation progression, including mean radius, biomass discharge ratio, total number, and bioparticle size distribution, were predicted well with the model. An optimum controlling strategy, automatically adjusted of settling time, was also proposed based on this model. Moreover, aerobic granules with a density higher than 120 g VSS/L and radius in a range of 0.4–1.0 mm were predicted to have both high settling velocity and substrate utilization rate, and the corresponding optimum operating conditions were be determined. Experimental results demonstrate that the developed model is appropriate for simulating the formation of aerobic granules in SBRs. These results are useful for designing and optimizing the cultivation and operation of aerobic granule process. Biotechnol. Bioeng. 2013; 110: 1312–1322. © 2012 Wiley Periodicals, Inc.