Fine-grained structures in Fe-36mass%Ni Invar alloy have been investigated by using transmission electron microscopy (TEM). Particular attention has been paid on the role of deformation twinning in the formation of fine-grained structures and its influence on tensile stress-strain behaviours of rolled specimens. In Fe-Ni Invar alloy with a moderate stacking fault energy, deformation twin did not appear in usual cold-rolling at room temperature (RT), where a kind of cell walls was formed and the Cu-type texture was observed. On the other hand, twinning was occurred by rolling when specimens were cooled to liquid nitrogen temperature (LNT) immediately before the rolling. In such case, a fine lamellar structure was developed and the brass-type texture appeared. However, the lamella boundaries did not coincide with any crystallographic planes, and they were intersected with the bands of deformation twin. Specimens rolled by 90% in thickness reduction exhibited tensile stress-strain behaviours similar to those observed in specimens with SPD structures. In particular, specimens rolled at LNT showed high yield strengths and non-uniform deformation.