The structure and electrical properties of two-dimensional (2D) sheets of silicon on a graphene substrate are studied using first-principles calculations. Two forms of corrugated silicon sheets are proposed to be energetically favorable structures. A shift of the Fermi energy level is found in both corrugated structures. Calculations of electron density show a weak coupling between the silicon layer and graphene substrate in both structures. The two forms of 2D silicon sheets turn out to be metallic and exhibit anisotropic transport properties. © 2013 AIP Publishing LLC.