To investigate the influence mechanism of the light-off characteristics and secondary pollutants (N₂O and NH₃) of the Pd/Rh catalytic converter for natural gas engines, a global model of the catalytic converter and a more comprehensive catalytic reaction mechanism were first established. Further, the model and the catalytic reaction mechanism were validated by using experimental data. Then, the effects of exhaust temperature and exhaust composition (H₂O, O₂, and H₂ concentrations) on the catalytic converters were investigated. The results showed that a higher temperature reduced the light-off time t50 of NO and CO. The production of N₂O decreased to 0 at high temperatures due to the reduction reactions of R14 (N₂O+H₂ = H₂O+N₂) and R16 (N₂O+CO = CO₂ + N₂). NH₃ would form at the temperature above 825 K, and the required H₂ originated from SR and WGS reactions. Increasing the H₂ concentration promoted the conversion of NO and CO. When the temperature exceeds 600 K, increasing the H₂ concentration decreases the production of N₂O. H₂O has the opposite effect on the production of N₂O and NH₃ at high temperatures. Increasing the content of H₂O increased the conversion of NO and inhibited the conversion of CO. O₂ concentration at 4000 × 10⁻⁶ is beneficial to reduce secondary pollutants of N₂O and NH₃. At the condition of 730–820 K and 4000 × 10⁻⁶ O₂, the productions of N₂O and NH₃ were reduced to 0. This study contributes to the efficient application of Pd/Rh catalytic converters and further enhances the emission reduction of natural gas engines.