Terahertz logic gates play a vital role in optical signal processing and terahertz digitization. Herein, a strategy to design an all-optical terahertz logic gate device composed of metamaterials with a semiconductor-metal hybrid is proposed; accordingly, a concrete logic gate composed of Ge embedded-in Au stripe supported by a Si board is presented theoretically. Simulation results reveal the dependence of the terahertz transmission spectra on the different illuminations in the device. Based on the illumination-transmission response, the designed device can realize the NOR or OR Boolean operation. The effects of the width of the Ge-Au stripe as well as the Si board on the transmission spectra and logic performance were also investigated.