Mechanical metamaterials exhibit unusual mechanical properties that originate from their topological design. Origami graphene may provide a platform for constructing novel carbon nanostructures. In the current study, a novel composite material that incorporates aligned graphene with localized origami shapes into the copper matrix is designed. Unlike many auxetic materials that have void phase, the proposed layer‐by‐layer assembled composite material appears to be solid in the microscopic scale. Based on the molecular dynamics (MD) simulations, it is observed that depending on the origami shapes, the in‐plane Poisson's ratio of origami graphene reinforced copper (100) composites can be tuned from positive to negative and, more importantly, it is discovered that the Young's modulus of the graphene/Cu composites can also be tuned from positive to negative in certain in‐plane directions.