Aerobic granules in a sequencing batch reactor (SBR) are subjected to alternative feast and famine conditions, and are able to take up carbon substrate in wastewater rapidly and to store it as intracellular storage products when the substrate is in excess. This phenomenon could not be described by the widely used activated sludge model No.3 (ASM3). In this work, taking adsorption process, microbial maintenance, and substrate diffusion into account, the simultaneous growth and storage processes occurring in an aerobic-granule-based SBR are investigated with experimental and modeling approaches. A new model is established and successfully validated with the experimental results of an SBR fed with soybean-processing wastewater. Simulation results show that our approach is appropriate for elucidating the fates of major model components. Comparison between ASM3 and the model established in this work demonstrates that the latter is better to describe the substrate removal mechanisms and simultaneous growth and storage processes in aerobic granules.