High broad-band photoresponsivity of mechanically formed InSe-graphene van der Waals heterostructures is achieved by exploiting the broad-band transparency of graphene, the direct bandgap of InSe, and the favorable band line up of InSe with graphene. The photoresponsivity exceeds that for other van der Waals heterostructures and the spectral response extends from the near-infrared to the visible spectrum.