The article provides a design of all-optical non-gate and NOR gate based on two-dimensional photonic crystal ring resonator structure. This design extracts the energy band structure of two-dimensional photonic crystals by plane wave expansion method and analyzes the steady-state electric field distribution of the device structure by the finite- time-domain difference method. The results demonstrate that the non-gate and NOR gate can achieve logic functions with a response period of 0.388 ps, a contrast ratio of 8.98 dB and 7.88 dB. The high extinction ratio and small structure sizes which are only 15.2 μm×15.2 μm and 13.984 μm×24.928 μm also contribute to convenient integration. The design with ring resonator makes optical logic gate devices more diverse, providing a basis for the optimal design of integrated circuits, and it also has important application research value.