A one-dimension aerobic granule mathematical model was established, basing on mathematical biofilm model and activated sludge model. The model was used to simulate simple aerobic granule process such as nutrients removal, granule diameter evolution, cycle performance as well as depth profiles of DO and biomass. The effluent NH4(+) -N concentration decreased as the modeling processed. The simulation effluent NO3(-)-N concentration decreased to 3 mg x L(-1) as the granules grew. While the granule diameter increased from 1.1 mm on day 30 to 2.5 mm on day 100, the TN removal efficiency increased from less than 10% to 91%. The denitrification capacity was believed to enhance because the anoxic zone would be enlarged with the increasing granule diameter. The simultaneous nitrification and denitrification occurred inside the big aerobic granules. The oxygen permeating depth increased with the consumption of substrate. It was about 100-200 microm at the beginning of the aeration phase, and it turned to near 800 microm at the end of reaction. The autotrophs (AOB and NOB) were mostly located at the out layer where the DO concentration was high. The heterotrophic bacteria were distributed through the whole granule. As hydrodynamic shear coefficient k(de) increased from 0.25 (m x d)(-1) to 5 (m x d)(-1), the granule diameter under steady state decreased form 3.5 mm to 1.8 mm. The granule size under the dynamic steady-state decreased with the increasing hydrodynamic shear force. The granule size could be controlled by adjusting aeration intensity.