In the magnetic sheets Fe-3%Si of HiB type, with AIN and MnS inhibitors, the Goss texture is obtained by a sudden and fast growth of the small size grains, with Goss orientation {1 1 0} < 0 0 1 >. This behaviour is not in good agreement with the classical laws of grain growth. In the present study, the abnormal grain growth is related to the material texture and to the texture component evolution, by carrying out Monte Carlo simulation. The onset of abnormal growth of Goss grains seems to be linked to the existence of a favourable crystallographic neighbourhood. The grains that grow abnormally do not have a size greater than the average size in the matrix; their ability to grow in an abnormal way can be related to the behaviour of grain boundaries, which surround them. The growth of a given grain is controlled by the local evolution of grain boundaries around that considered grain and not by the average evolution of the totality of the matrix; the whole effect of the matrix can hide the effect of matrix heterogeneity. The experimental characterisation of matrix parameters is performed by Electron Back Scattering Diffraction (EBSD). (C) 2004 Elsevier B.V. All rights reserved.