A narrowband radiation model is coupled to the OPPDIF program, which uses detailed chemical kinetics and thermal and transport properties to enable the study of one-dimensional counterflow H2/O2 diffusion flames with CO2 as dilution gas over the entire range of flammable strain rates. The effects of carbon dioxide dilution, ambient pressure and inlet temperature of opposed jets on the extinction limits and flame structures are compared and discussed. The extinction limits are presented using maximum flame temperature and strain rate as coordinates. Both high-stretch blowoff and the low-stretch quenching limits are computed. When the CO2 dilution percentage is higher, the flame is thinner and flame temperature is lower. The combustible range of strain rates is decreased with increasing CO2 percentage due to the effects of CO2 dilution, which is categorized as dilute effect, chemical effect and radiation effect. In addition, the flame temperature of low-stretch diffusion flame with radiation loss is substantially lower than that computed with the non-radiation model. This large temperature drop results from the combined effect of flame radiation and chemical kinetics. The extinction limits and flame temperature are increasing with increasing atmospheric pressure and temperature, but the flame thickness is decreased with the pressure. At higher pressure and temperature, the extinction limits are extended more on the high-stretch blowoff limits, indicating the influence of the ambient pressure and temperature on the chemical reaction.