The objective of this article is to clarify the effect of thermal and equivalence ratio stratification on Homogeneous Charge Compression Ignition (HCCI) combustion under several conditions with three-dimensional computational fluid dynamics (3D CFD). Reynolds Averaged Navier-Stokes (RANS) simulation was used to calculate in-cylinder fluid dynamics. The 3D CFD simulation is also coupled with detailed chemical reaction to calculate HCCI combustion. First, the study with a simple engine model reveals that thermal stratification is more effective for prolonged combustion duration, which is a key factor for a high load limit of HCCI combustion, than equivalence ratio stratification. Thermal stratification has two-stage combustion: the combustion propagates from hot region slowly at first and then ignites in the entire in-cylinder region. Owing to this phenomenon, thermal stratification is more effective to mitigate HCCI combustion. Furthermore, thermal stratification enables combustion efficiency to be maintained: combustion efficiency would be a problem to relieve HCCI combustion by intake charge stratification. Second, the study with a detailed engine model was conducted to evaluate the improvement of the high load limit and thermal efficiency under the constraint of the maximum in-cylinder pressure and the pressure rise rate. In the second study, mixture stratification was produced by inducting hot and cold intake mixture from respective intake ports. The result shows that the temperature of in-cylinder hot gas region plays an important role to extend the high load limit of HCCI combustion.