Three-way catalysts (TWCs) have been widely used on stoichiometric gasoline and natural gas engines for CO, hydrocarbons and NOx emissions control. Oxygen storage capacity (OSC) is a critical factor of a TWC and is closely related to the catalyst aging and performance. On natural gas engine aftertreatment development, on-board diagnostic (OBD) is required and OSC monitoring is the primary TWC OBD method. A dynamic OSC model involving two storage sites with distinct kinetics was developed and validated on the engine. The validated OSC model was utilized to study the effects of engine operating conditions (oxygen concentration and space velocity) on lean breakthrough OSC (OSB), which is monitored through OBD. Base on the simulation analysis, it was found that OSB is not a constant for a particular TWC catalyst and is dependent on space velocity and oxygen concentration. The breakthrough OSC increases slightly with oxygen concentration and increases significantly as space velocity decreases. In addition, OSB is limited by the amount of “fast OSC” at high space velocity and limited by the amount of accessible “slow OSC” at low space velocity. Moreover, oxygen breakthrough was not observed under extremely low space velocity in the model, which was consistent with the experimental results on the engine. Eventually, correlations of oxygen breakthrough time and OSB were established based on oxygen concentration and space velocity, which can be applied in TWC OBD algorithm development.