Micro-corona devices could be extensively utilized in gas sensing, switchgear, biomedicine, and other fields. As the influence mechanism of the cathode curvature radius on micro-corona discharge dynamical processes is very important for performance optimization and the promotion of these devices, a micro-scale corona discharge gas model in a mixture of N2-O2 is proposed based on the fluid–chemical mixing method, which describes the dynamic process of the discharge at atmosphere and normal temperatures. To reveal the influence mechanism of the nanowire curvature radius on the micro-corona discharge, the effect of the cathode nanowire radius on the discharge current, electric field, ionization reaction rate, and charged particle characteristics at different gaps and voltages were determined. The findings indicate that the effect of curvature radius on discharge intensity varies under different gap and voltage conditions. Further analysis indicates that an increase in curvature radius reduces the electric field near the tip while increasing the ionization area and secondary emission area as well as the number of positive ions in the space, consequently affecting the coupling process between the collision ionization and the secondary emission. Especially under the conditions of either small gap or low voltage, a suitable increase in the curvature radius could promote the coupling process and then increase the discharge current.