In a pre-chamber engine, fuel in the main-chamber is ignited and combusted by the combustion gas injected from the pre-chamber. Therefore, further fuel dilution is possible and thermal efficiency can be also improved. However, adding a pre-chamber to an engine increases the number of design parameters which have a significant impact on the main combustion and the exhaust gas. Then, in this study, the optimum geometry of the pre-chamber in an active pre-chamber gas engine was investigated. The considered parameters were the volume of pre-chamber, the diameter of a nozzle hole, and the number of nozzle holes. 18 types of pre-chambers with different geometries were prepared. Using these pre-chambers, engine experiments under steady conditions were conducted while changing the conditions such as engine speeds, mean indicated pressure and air excess ratio. Based on the experimental data, neural network models were constructed that predict thermal efficiency, NOx and CO emissions from the pre-chamber geometries and the engine operation conditions. Employing these models as objective function, the optimal geometry of the pre-chamber is obtained as Pareto solutions. The availability of this method to determine the optimal geometry of pre-chamber was proved since the general trade-off relationship between thermal efficiency and NOx was shown.