We show how the N = 2 super-W∞ algebra can be twisted to give a topological algebra, which we call W∞top. This can be realised by a matter system comprising a complex scalar and a complex spinor field. We construct a topological BRST charge for W∞top, and use this to obtain a topological W∞ gravity theory. This can then be coupled to the W-topological matter system. The total lagrangian arises as a BRST variation.