In the present work, a nanocrystalline Invar alloy (Fe-36wt%Ni) foil was fabricated by using a continuous electroforming method. This material exhibited outstanding mechanical properties and a relatively low thermal expansion coefficient as compared to conventional Invar alloys. The as-deposited texture was of fibre-type characterized by strong <100>//ND and weak <111>//ND components. Grain growth occurred during annealing beyond 350degreesC and resulted in such texture change that the <111>//ND fibre texture strongly developed with the minor <100>//ND components. It was clarified using orientation imaging microscopy that abnormal growth of the <111>//ND grains in the early stages of grain growth plays an important role on the texture evolution. The mechanism of the abnormal grain growth has been discussed in terms of the orientation dependence of energy density.