A wheat variety designated W011031I1, the plants and seeds of wheat variety W011031I1, methods for producing a wheat plant produced by crossing the variety W011031I1 with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety W011031I1 with another wheat line or plant, and the creation of variants by mutagenesis or transformation of variety W011031I1. This invention also relates to methods for producing other wheat varieties or breeding lines derived from wheat variety W011031I1 and to wheat varieties or breeding lines produced by those methods.