Direct numerical simulation (DNS) of turbulent flow through an asymmetric plane diffuser, which consists of flat and inclined walls, was carried out using a high-order finite difference method, in order to establish a database for non-equilibrium turbulence in the adverse pressure gradient. Typical feature of this flow field is the unsteady three-dimensional reverse flow region in the inclined wall side. At the beginning of the diffuser, low speed streaks in the wall turbulence cause the first unsteady separation which includes small-scale reverse flow regions. Following this region, because the turbulent eddy growing from the first unsteady separation suppresses the separated flow, a small reattachment section is formed in the downstream of the first unsteady separation. When the turbulent eddy declines and the adverse pressure gradient becomes dominant, the flow tends to separate again. And then, a large scale separation region is formed. In summary, the intensity of the turbulent eddy affects the formation of the separation and reattachment region on the inclined wall.