Grain growth in 2D polycrystals was simulated under the supposition that triple junctions possess a restricted mobility and so impede the migration of grain boundaries. A parameter 0 L = 0 D m taking into account the effect of triple junctions was varied in the range from 0.003 to 270 (m is the ratio of the triple junction mobility to that of grain boundary and 0 D the initial grain diameter). It was shown that at 0 L <0.4–0.5, i.e. at a small 0 D and small m, the growth kinetics becomes linear. It is supposed that the effect of triple junctions on grain growth can be observed in nanocrystalline materials.