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Grain growth can modify the microstructure of natural ice, including the grain size and crystallographic preferred orientation (CPO). To understand better grain-growth processes and kinetics, we compared microstructural data from synthetic and natural ice samples that were annealed at ice-solidus temperature (0°C) to successfully long durations. The synthetic ice has a homogeneous initial microstructure, which is characterised by polygonal grains, little intragranular distortion and bubble content, and a near-random CPO. The natural ice samples were sub-sampled from ice cores acquired from the Priestley Glacier, Antarctica; they have a heterogeneous microstructure, which is characterised by a considerable number of air bubbles, widespread intragranular distortion, and a preferred crystallographic alignment. During annealing, the average grain size of natural ice barely changes, whilst the average grain size of synthetic ice gradually increases. This observation suggests grain growth in natural ice can be much slower than synthetic ice; the grain-growth law derived from synthetic ice data cannot be directly applied to estimate the grain-size evolution in natural ice. The microstructure of natural ice characterised by many bubbles pinning at grain boundaries. Previous studies suggest bubble pinning reduces the driving force of grain boundary migration, and it should be directly linked to an inhibition of grain growth observed in natural ice. As annealing progresses, the number density (number per unit area) of bubbles on natural-ice grain boundaries decreases, whilst the number density of bubbles in grain interior increases. This observation indicates that some ice grain boundaries sweep through bubbles, which should weaken the bubble-pinning effect and thus enhance the driving force for grain boundary migration. Consequently, the grain growth in natural ice might comprise more than one stage and it should correspond to more than one set of grain-growth parameters. Some of the Priestley ice grains become abnormally large during annealing. We suggest the bubble-pinning, which inhibits the grain growth of ice matrix, and the contrast of dislocation-density amongst neighbouring grains, which favours the selected growth of individual grains with low dislocation densities, are tightly correlated with the abnormal grain growth. [ABSTRACT FROM AUTHOR]