For the development of Si-based next generation electronic-photonic integrated circuits, a silicon optical modulator is designed based on tunable plasmonic directional couplers. The characteristics are investigated using numerical simulations with a full-vectorial beam propagation method. The center waveguide in the three-core coupler is a MOS-type hybrid plasmonic waveguide that consists of a Si-ITO-SiO2-Si structure. By electrically tuning the ITO's refractive index, the coupling efficiency of the directional coupler is switchable and, hence, we can obtain modulated optical signals at the outer waveguide, which is configured with a vertical offset. The extinction ratios are 6.7 and 2.3 dB at 1.31- and 1.55-μm wavelength, respectively. The optical modulator can be transformed into a plasmonic absorption modulator based on a two-core directional coupler at the cost of a long coupling length. The proposed silicon optical modulator has the potential to play a key role in complementary metal-oxide-semiconductor-compatible 3-D silicon photonic integrated circuits.