Aerobic granules were cultivated in a sequencing batch reactor (SBR) fed with soybean-processing wastewater at 25+/-1 degrees C and pH 7.0+/-0.1. The granulation process was described via measuring the increase of sludge size. The formation of granules was found to be a four-phase process, that is, acclimating, shaping, developing, and maturated. A modified Logistic model could well fit with the granule growth by diameter and could be employed to estimate the maximum diameter, lag time, and specific diameter growth rate effectively. Both normal and log-normal distributions proved to be applicable to model the diameter distribution of the granules. The granule-containing liquor was shear thinning, and their rheological characteristics could be described by using the Herschel-Buckley equation. The suspended solids concentration, pH, temperature, diameter, settling velocity, specific gravity, and sludge volume index all had an effect on the apparent viscosity of the mixed liquor of granules. The matured granules had fractal nature with a fractal dimension of 1.87+/-0.34. Moreover, 83% of matured granules were permeable with fluid collection efficiencies over 0.034. As compared to activated sludge flocs, the aerobic granules grown on the soybean-processing wastewater had better settling ability, mass transfer efficiency, and bioactivity.