In this study we investigated the characteristics of fluid flow and heat transfer within a coolant passage in the cylinder head assembly of an internal combustion engine by using a commercial CFD code, CFX The complex coolant passage of the cylinder head assembly was modelled by suitable choice of a grid system and careful attention was paid in the construction of meshes near the walls where significant cooling occurs. To treat the simultaneous heating and cooling of the combustion walls we invented a methodology allowing a heat source within the solid wall and the convective cooling at the interface between the solid and the fluid. We managed to reproduce the experimental results by adjusting parameters appropriately. We have found that high temperature was concentrated at the surface of the cylinder jacket. It turned out that the effect of oil cooling from the piston head was unexpectedly significant. On the other hand the effect of cooling from the ambient air is almost negligible. The CFD method proposed in this study is believed to be useful in the early stage of the design of the engine-cooling system.