Highly selective etching of silicon nitride (Si3N4) and silicon dioxide (SiO2) has received considerable attention from the semiconductor community owing to its precise patterning and cost efficiency. We investigated the etching selectivity of Si3N4 and SiO2 in an NF3/O2 radio-frequency glow discharge. The etch rate linearly depended on the source and bias powers, whereas the etch selectivity was affected by the power and ratio of the gas mixture. We found that the selectivity can be controlled by lowering the power with a suitable gas ratio, which affects the surface reaction during the etching process. X-ray photoelectron spectroscopy of the Si3N4 and QMS measurements support the effect of surface reaction on the selectivity change by surface oxidation and nitrogen reduction with the increasing flow of O2. We suggest that the creation of SiOxNy bonds on the surface by NO oxidation is the key mechanism to change the etch selectivity of Si3N4 over SiO2.