Functional and structural imaging studies have demonstrated the involvement of the brain in balance control. Nevertheless, how decisive grey matter density and white matter microstructural organisation are in predicting balance stability, and especially when linked to the effects of aging, remains unclear. Standing balance was tested on a platform moving at different frequencies and amplitudes in 30 young and 30 older adults, with eyes open and with eyes closed. Centre of pressure variance was used as an indicator of balance instability. The mean density of grey matter and mean white matter microstructural organisation were measured using voxel-based morphometry and diffusion tensor imaging, respectively. Mixed-effects models were built to analyse the extent to which age, grey matter density, and white matter microstructural organisation predicted balance instability. Results showed that both grey matter density and age independently predicted balance instability. These predictions were reinforced when the level of difficulty of the conditions increased. Furthermore, grey matter predicted balance instability beyond age and at least as consistently as age across conditions. In other words, for balance stability, the level of whole-brain grey matter density is at least as decisive as being young or old. Finally, brain grey matter appeared to be protective against falls in older adults as age increased the probability of losing balance in older adults with low, but not moderate or high grey matter density. No such results were observed for white matter microstructural organisation, thereby reinforcing the specificity of our grey matter findings.