The aim of this study is to clarify the mixture formation in the combustion chamber of our developed natural gas engine incorporating the sub-chamber injection system, in which natural gas is directly injected into a combustion sub-chamber in order to completely separate rich mixture in the sub-chamber, suitable for ignition, from ultra-lean mixture in the main chamber. Mixture distributions in chambers with and without sub-chamber were numerically simulated at a variety of operating conditions. The commercial software of Fluent 16.0 was used to conduct simulations based on Reynolds averaged Navier-Stokes equations in an axial 2 dimensional numerical domain considering movements of piston. Non-reactive flow in the combustion chamber was simulated before the ignition timing at an engine speed of 2000 rpm. The turbulence model employed here is standard k-ε model. Air-fuel ratio is set with a lean condition of 30. The results obtained from the numerical simulations demonstrate higher equivalence ratio in the sub-chamber than that in the main chamber, which extends the lean limit at engine operations. Furthermore, existing probability of mixture with low equivalence ratio is higher than that without the sub-chamber, which is an evidence of lower NOx emissions from test engines incorporating the sub-chamber. On the other hand, high equivalence ratio mixture remains in the squish area of the main chamber when the sub-chamber is installed. The unburned fuels in the squish area probably cause high hydrocarbon emissions from engines, observed during engine tests. In addition, the retarded timing of injection end results in the accumulation of fuel in the sub-chamber, increasing the equivalence ratio of mixture existing in the sub-chamber. The high hydrocarbon emissions observed during engine tests under retard conditions are due to the deterioration of ignitability resulting from the richer mixture.