The texture evolution that takes place during annealing was investigated in a nanocrystalline Fe-78wt%Ni permalloy fabricated by using an electrodeposition method. The as-deposited texture was characterized by a strong <100>//ND fibre and a weak <111>//ND fibre. Grain growth occurred during annealing beyond 340degreesC and resulted in the texture change that the <111>//ND fibre strongly developed at the expense of the <100>//ND fibre. It was observed using orientation image microscopy that the <111>//ND oriented grains abnormally grew in the early stages of grain growth. The relationship between the texture evolution and the microstructural change during annealing is interpreted and discussed in terms of the orientation dependency of grain growth.