A compact electro-optical “NOR” logic gate device based on silicon-on-insulator (SOI) platform is proposed and investigated theoretically. By introducing a hook-type waveguide, the signal could be coupled between the bus and hook-type waveguide to form an optical circuit and realize NOR logic gate. We can easily realize the NOR logical function by the voltage applied on the coupling components. The numerical simulation shows that a high coupling efficiency of more than 99% is obtained at the wavelength of 1550 nm, and the footprint of our device is smaller than 90 μm2. In addition, the response time of the proposed NOR logic gate is 3 ns with a switching voltage of 1.8 V. Moreover, it is demonstrated that such NOR logic gate device could obtain an extinction ratio of 21.8 dB. Thus, it has great potential to achieve high speed response, low power consumption, and small footprint, which fulfill the demands of next-generation on-chip computer multiplex processors.