Calibre rolling of Mg-3Al-1Zn alloy at 300 °C led to development of fine grain size of 3 μm. Subsequent annealing, from 5 to 6000 minutes at 300-450 °C, revealed faster grain growth initially up to 60 minutes, which became sluggish on prolonged annealing. The time exponent for grain growth kinetics (n) suggests bi-linear behaviour with n = 0.11 and 0.008 over these time scales. The activation energy, based on various n values, varied over wide ranges that made the understanding of the mechanisms for grain growth difficult. This problem is explained by concurrent evolution of texture and grain boundary structure. The effect of grain growth on hardness at ambient temperature was found to follow the H-P type relationship. © 2015.