Streamer discharge has been widely used in fields of sterilization, disinfection, ozone generation, etc. The secondary discharge process significantly affects the effective ozone production duration and efficiency. However, the mechanism of oxygen concentration affecting secondary discharge characteristics and the yield of target products is still unclear. To address this issue, a fluid-based analysis model of the secondary positive streamer discharge process between needle-plate electrodes under varying oxygen concentrations is developed in this work. This model considers the radial electric field and resolves potential non-physical branching issues that may arise in discharge simulations at high oxygen concentrations. In this work, the effect of oxygen concentration on the optical emission characteristics of secondary positive streamers is examined. The optical emission intensity, cathode charge transfer, and the yields of excited-state oxygen atoms (O(³P)) under different oxygen concentrations are investigated and compared with experimental data. The results show that when the oxygen concentration increases from 20% to 90%, the light emission intensity of the secondary discharge decreases by about 0.2%. At the same time, the average electron density in the discharge channel decreases by 90%, the change of electric field intensity is less than 10%, and the duration of single discharge duration is shortened by 77%. Under these conditions, the proportion of O(³P) yield originating from the primary discharge increases from 20% to 38%, and the unit energy yield of excited-state oxygen atoms O(³P) rises by 64%. Although the reduction in discharge duration results in a 50% decrease in absolute O(³P) yield, the increase in unit energy yield far compensates for the decrease in single-discharge yield. The single-discharge yield decreases with oxygen concentration increasing due to the enhanced two- and three-body adsorption effects of oxygen molecules, which reduce the electron density. Additionally, the increased collision probability between electrons and oxygen molecules further affects these characteristic changes.