We report a terahertz optical modulator consisting of randomly stacked trilayer graphene (TLG) deposited on an oxidized silicon substrate by means of THz-Time Domain Spectroscopy (THz-TDS). Here, the gate tuning of the Fermi level of the TLG provides the fundamental basis for the modulation of THz transmission. We measured a 15% change in the THz transmission of this device over a broad frequency range (0.6-1.6 THz). We also observed a strong absorption >80% in the time-domain signals and a frequency independence of the conductivity. Furthermore, unlike previous studies, we find that the underlying silicon substrate, which serves as a gate electrode for the graphene, also exhibits substantial modulation of the transmitted THz radiation under applied voltage biases.