Recent theoretical and experimental studies demonstrated that breaking of the sublattice symmetry in graphene produces an energy gap at the former Dirac point. We describe the synthesis of graphene sheets decorated with ultrathin, Si-rich two-dimensional (2D) islands (i.e., Gr:Si sheets), in which the electronic property of graphene is modulated by coupling with the Si-islands. Analyses based on transmission electron microscopy, atomic force microscopy, and electron and optical spectroscopies confirmed that Si-islands with thicknesses of ~2 to 4 nm and a lateral size of several tens of nm were bonded to graphene via van der Waals interactions. Field-effect transistors (FETs) based on Gr:Si sheets exhibited enhanced transconductance and maximum-to-minimum current level compared to bare-graphene FETs, and their magnitudes gradually increased with increasing coverage of Si layers on the graphene. The temperature dependent current-voltage measurements of the Gr:Si sheet showed approximately a 2-fold increase in the resistance by decreasing the temperature from 250 to 10 K, which confirmed the opening of the substantial bandgap (~2.5-3.2 meV) in graphene by coupling with Si islands.